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The nonlinear forced vibration behavior of truncated open conical nanoshells is investigated in this paper. Nonlocal elasticity theory has been employed to modify the size-dependent effect of micro/nanostructure. Von Karman nonlinear strains are used to consider the geometric nonlinearity of the nanoshells. Using Hamilton's principle, the equations of motion and boundary conditions of truncated open conical nanoshells are derived. Galerkin method is used to solve the governing equations. Then, to determine the nonlinear forced vibration behavior of truncated open conical nanoshells, complex averaging and arc-length continuation methods are employed. Finally, the effect of nonlocal parameters, cone apex angle, the amplitude of harmonic excitation, structural damping coefficient, and geometrical parameters on the nonlinear frequency response of the truncated open conical nanoshells are discussed. [ABSTRACT FROM AUTHOR]

The capillary effect acts a key role in our daily life, and its vibration can significantly affect its mass transmission. Here, we aim to study the vibration of the capillary in a nanoscale deformable tube. First, we present the mathematical model, and then we give a detailed study on its vibration characteristics by means of the Hamiltonian‐based method, which is based on the variational principle and Hamiltonian. In the view of the energy conservation, the residual equations are introduced to determine the frequency‐amplitude formulation. We finally verify the effectiveness and reliability of the proposed method by comparing with existing method through the numerical results. The finding in this work is expected to be helpful for the study of the nonlinear vibration. [ABSTRACT FROM AUTHOR]

This is a unique study in which a damped porous microplate's nonlinear vibration and response are analyzed semi-analytically using MSGT and HSDT under localized loading. The substrate is modeled using the Winkler-Pasternak elastic foundation. Partial differential equations are obtained using Hamilton's principle and solved by Galerkin's method. IHB and Newmark's methods are used to trace the nonlinear vibration and response. The results show that uniform porosity leads to lower stiffness compared to symmetric porosity distribution. Pasternak foundation parameter has a larger impact on stiffness compared to Winkler parameter. The effect of geometric nonlinearity is weakened while using MSGT. [ABSTRACT FROM AUTHOR]

This research explores the efficacy of integrating nonlinear single-degree-of-freedom systems in the vibration control of rod coupling systems. By interlinking two rods with a nonlinear single-degree-of-freedom system as the intermediary, the study employs the Lagrange method (LM) to forecast nonlinear vibrational behaviors. The findings, substantiated by numerical analyses, affirm the precision of LM in gauging the amplitude responses when such a nonlinear system is utilized. The nonlinear dynamics, characterized by intricate vibrational patterns, peak jumping phenomena, and the migration of resonance zones, are induced by the nonlinear single-degree-of-freedom system. By fine-tuning the system's parameters, significant alterations in the vibrational states of the rod coupling system are achievable. This suggests that the application of a nonlinear single-degree-of-freedom system is a viable strategy for modulating vibrations in rod systems. Furthermore, optimal parameterization of this system is proven to effectively dampen vibrations, showcasing its potential as a sophisticated mechanism for vibration suppression in coupled rod configurations. [ABSTRACT FROM AUTHOR]

A new control approach based on fuzzy sliding mode control (FSMC) is proposed to regulate the chaotic vibration of an axial string. Hamilton's principle is used to formulate the nonlinear equation of motion of the axial translation string, and the von Kármán equations are used to analyse the geometric nonlinearity. The governing equations are nondimensionalized as partial differential equations and transformed into a nonlinear 3-dimensional system via the third-order Galerkin approach. An active control technique based on the FSMC approach is suggested for the derived dynamic system. By using a recurrent neural network model, we can accurately predict and effectively apply a control strategy to suppress chaotic movements. The necessity of the suggested active control method in the regulation of the nonlinear axial translation string system is proven using different chaotic vibrations. The results show that the study of the chaotic vibrations of axially translating strings requires nonlinear multidimensional dynamic systems of axially moving strings; the validity of the proposed control strategy in controlling the chaotic vibration of axially moving strings in a multidimensional form is demonstrated. [ABSTRACT FROM AUTHOR]

To study the nonlinear dynamic behavior and system stability of a rubbing overhung rotor with viscoelastic and memory-effect damping and random uncertain parameters, this paper introduces a fractional-order modeling and stochastic dynamic analysis method for the nonlinear overhung rotor system with frictional impact faults. Firstly, the dynamic equations of the overhung rotor considering friction effect and fractional damping effect are established based on the transfer matrix method and fractional order derivative. Then, the time-domain response of the fractional-order dynamic equations is solved by combining the Runge–Kutta method and the continuous fractional expansion, and the steady-state response characteristics of different fractional damping are analyzed in the deterministic case. Finally, to analyze the response of the system under the effect of stochastic parameters, the sparse grid-based PCE metamodel of the system response is developed. Statistical moments, probability distributions, and sensitivity indices of the response of stochastic systems are revealed. The results of this paper provide a theoretical basis for efficient and accurate prediction of the stochastic response of nonlinear rubbing overhung rotor systems. [ABSTRACT FROM AUTHOR]

To clarify the motion characteristic of the drill string in deviated well, the nonlinear dynamic model of lateral-torsional coupling for drill string system is established by the Lagrange equation. This model incorporates the contact between the drill string and borehole wall, torque dissipation, and borehole trajectory effects. Additionally, the contact behavior using linear elastic contact model is simulated. Meanwhile, the torque transfer law in the drill string system is described by a discrete torque-drag model. Finally, numerical simulations are employed to determine the dynamic properties of the drill string system. The results reveal that friction losses in drill string systems are increased with higher well inclination angles. The motion of BHA along the x direction is predominantly concentrated near the wellhole center at inclination angle of 65°, while in the x direction it primarily focuses on the low side of the wellhole. An increase in inclination angle leads to a more prominent occurrence of stick-slip motion in the drill string. When inclination angle more than 25°, there is a slightly higher collision frequency observed between the BHA and the low side of the borehole wall compared to that with the upper side. When increasing the WOB (weight on bit) to 160 kN, stick-slip motion becomes more pronounced within the drill string. Through parametric dynamics analysis of the drill string system, the rotary speed can be controlled in range from 40 to 70 r/min, and the WOB should be restricted in range from 20 to 40 kN in well depth 5000 m. [ABSTRACT FROM AUTHOR]

Aeroengine power turbine rotor is a typical nonlinear rotor system, in which the interference connection between long shaft and short shaft has a prominent influence on the coupling vibration of the system, especially at high speed, the nonlinear stiffness change of interference contact is more obvious. Therefore, the paper considers the change of the contact characteristics of the long shaft and the short shaft of the turbine rotor, and the nonlinear restoring force of the bearing to analyze the dynamic characteristics of the rotor. Firstly, according to the theory of elasticity, the contact parameters under different speed states are calculated, the contact stiffness model under interference fit is established, and the relationship between contact stiffness and speed is analyzed. Secondly, according to the Hertz contact theory, a bearing nonlinear restoring force model considering time-varying characteristics is established. Finally, the dynamic model of the bearing-flexible rotor coupling considering interference contact is established. The influence of contact parameters and unbalance parameters on the nonlinear vibration characteristics of the rotor is analyzed by amplitude-frequency curve, bifurcation diagram, time-domain waveform, spectrum diagram, trajectory diagram and Poincaré diagram. In addition, the simulation results are compared with the experiment results of the rotor test rig to verify the accuracy of the established dynamic model. By analyzing the influence of different parameters such as interference magnitude, unbalance position, unbalance magnitude and unbalance couple on the nonlinear vibration of the rotor, the basis for the design and vibration control of the cantilever turbine rotor is provided. [ABSTRACT FROM AUTHOR]

Functionally graded graphene nanoplatelet reinforced composite (FG-GNPRC) have exhibited significant potential for the development of high-performance and multifunctional structures. In this paper, we present a machine learning (ML) assisted uncertainty analysis of nonlinear vibration of FG-GNPRC membranes under the influence of multi-factor coupling. Effective medium theory (EMT), Mori-Tanaka (MT) model and rule of mixture are utilized to evaluate the effective material properties of the composite membrane. Governing equations are derived via an energy method with the frameworks of the hyperelastic membrane theory, Neo-Hookean constitutive model and the couple dielectric theory. Randomly generated inputs after data pre-processing are fed into governing equations, which are solved by numerical methods for outputs. Three ML models, including artificial neural network (ANN), support vector regression (SVR) and AutoGluon-Tabular (AGT), are adopted to capture the complex relationship between the systematic inputs (i.e., structural dimensions, attributes of GNPs and pores, external electric field, etc.), frequency ratio and dimensionless amplitude of FG-GNPRC membranes. The results demonstrate that all three ML models demonstrate exceptional computational efficiency, and AGT presents higher prediction accuracy compared to the other two models. Based on the Shapley additive explanations (SHAP) approach, the effects of uncertainties of system parameters and multi-factor coupling on the nonlinear vibration of the FG-GNPRC membrane are analyzed. It is found that the uncertainty of structural parameters has the greatest impact on the nonlinear vibration of FG-GNPRC membranes, particularly when the membrane is subjected to a voltage of 10 V and smaller stretching ratio. [ABSTRACT FROM AUTHOR]

Nonlinear free vibration and dynamical responses of carbon nanotube (CNT) reinforced composite beams with surface-bonded piezoelectric layers and tangentially restrained ends under thermo-electro-mechanical loads are investigated in this paper. The properties of constitutive materials are assumed to be temperature-dependent and effective properties of nanocomposite are estimated using an extended rule of mixture. Unlike previous studies, the present work considers the effects of tangentially elastic constraints of two ends on the nonlinear dynamic characteristics of hybrid beams. Motion equation is established within the framework of Euler-Bernoulli beam theory taking into account von Kármán nonlinearity. Analytical solution is assumed to satisfy simply supported boundary conditions and Galerkin procedure is employed to obtain a time ordinary differential equation including both quadratic and cubic nonlinear terms. This differential equation is numerically solved employing fourth-order Runge-Kutta scheme to determine the frequencies of nonlinear free vibration and nonlinear transient response. Parametric studies are executed to examine numerous influences on the nonlinear dynamical characteristics of hybrid nanocomposite beams. The study reveals that tangential constraints of ends substantially effect the frequencies and dynamic response of the beam, especially at elevated temperatures. The results also indicate that nonlinear dynamic responses can be controlled effectively by means of piezoelectric actuators and elasticity of tangential constraints of ends should be considered in design of piezo-CNTRC beams. [ABSTRACT FROM AUTHOR]

Nonlinear energy sink (NES) as a new type of dynamic absorber has received widespread attention due to its broadband vibration suppression capability, but it has a certain requirement of energy triggering threshold. In this work, a bistable NES-based piezoelectric system with combined damping (BCPNES) and low threshold requirement is proposed. Electromechanical-coupled equations for the nonlinear oscillator coupled with BCPNES (NO-BCPNES) are established. The vibration suppression and vibration energy harvesting performance for the coupled system are investigated numerically and analytically. The frequency–energy plots of the conservative system are investigated using the complex-variable averaging method and the electromechanical decoupling method. The influence of circuit parameters on the target energy transfer threshold and harvested energy is discussed through the equivalent stiffness and damping of the circuit. The vibration suppression performance and the target energy transfer characteristics are analyzed in terms of the time–history response, the time–frequency response and the slowly varying dynamic flow, respectively. The results show that the electromechanical coupling coefficient affects the skeleton curve of frequency–energy plots in the form of equivalent stiffness. The NO-BCPNES system exhibits higher energy dissipation performance and better targeted energy transfer form under various excitations. From the phase perspective, NES-based piezoelectric system achieves vibration suppression of the main structure through the phase locking phenomenon. The mechanism of the influence of piezoelectric device parameters on the energy harvesting performance of the systems is clarified. [ABSTRACT FROM AUTHOR]

The bistable morphing composite laminated shell presents promising potential for aerospace morphing structures design, as it is capable of shape-changing under small energy inputs and maintaining two stable states without external loading. The bistable nonlinearity is distinct from the typical geometrical nonlinearity, as it arises from thermal residual stresses that cannot be equalized. During the derivation of a three-degree-of-freedom nonlinear dynamic model, Sanders' nonlinear strain is incorporated into the strain–displacement relationship, while thermal residual stresses are taken into account in the constitutive relationship. The nonlinear dynamic model effectively captures the snap-through phenomena with orthogonal asymmetry in bistable morphing composite laminated shells. In order to reveal the resonance response and chaotic characteristics due to the interaction of vibrations between degrees of freedom, high-dimensional nonlinear dynamical model is derived by multiple scales method based on the 1:1:1 internal resonance relationship. The resonance response curves reflect the parametric influence law of the dynamical system stability. The nonlinear dynamic behaviors are described by the bifurcation diagrams and the maximum Lyapunov exponent. The significant motions under particular excitation conditions are visualized by phase portraits, time histories and Poincaré maps. [ABSTRACT FROM AUTHOR]

In this study, nonlinear vibrations and stability of multilayer functionally graded (FG) pipes conveying fluid laying on nonlinear elastic foundation and reinforced by graphene nanoplatelets (GPLs) are investigated with an emphasis on optimized analytical method. Various types of GPL distribution patterns are considered and to estimate the mechanical characteristics of the reinforced pipe the Halpin–Tsai micromechanics theory is applied. The nonlinear differential equation of motion is obtained by using Von–Kármán strain relations in conjunction with the Euler–Bernoulli beam theory and applying Hamilton's principle. The Galerkin technique has been used for discretizing the partial differential equation. The optimized homotopy analysis method (HAM), as a strong analytical method, is utilized to solve the nonlinear differential equation by considering different initial excitations. The convergence-control parameter is taken into account to guarantee the convergence of the analytical solution. In this study, an exact solution based on HAM for the critical flow velocity and n th nonlinear frequency is presented. Additionally, series solutions for the nonlinear time responses of the transverse and longitudinal vibrations of fluid-conveying pipe based on optimized HAM are obtained for the first time. In the numerical results, the effects of arbitrary initial conditions and different physical characteristics on the nonlinear frequencies and time responses are extensively examined. It is shown that the nonlinear frequencies and critical flow velocity of the pipe depend not only on the initial excitation amplitude, but also on the entire initial excitation function applied on the pipe. [ABSTRACT FROM AUTHOR]

The phenomenon of stiffness hardening has detrimental influence on the natural frequency and the width of vibration isolation frequency bands, which significantly confines the development of quasi-zero-stiffness vibration isolators (QZSVIs). To overcome this restriction, the nonlinear mirrored-stiffness design method (NMSM) is proposed and its applicable condition is revealed. Based on the mechanism of stiffness hardening, a nonlinear spring (NS) is designed by the NMSM. NS possesses nonlinear restoring force and a mirror-image relationship with the targeted negatives stiffness. The mathematical model of the NS is established based on Heaviside function. Coupled QZSVIs (CQZSVIs) are constructed by a concave metastructure with multiple stiffness properties and the NS to validate the NMSM. A prototype of the CQZSVI is fabricated to prove the correctness of the theoretical analysis. The practical tests of the CQZSVI demonstrate an obvious QZS region where the restoring force remains approximately constant and the stiffness is almost invariable and close to zero. The results of sweep-frequency experiments show that the CQZSVI has a natural frequency of about 0.8 Hz and a broad effective vibration isolation region starting from about 1.1 Hz. Its transmissibility is about − 15 dB at 3 Hz and is about − 20 dB at 3.5 Hz. The NMSM successfully breaks through the bottleneck of the development of QZSVIs and produces a new approach for the construction of low-frequency vibration isolators. [ABSTRACT FROM AUTHOR]

AbstractThe significant dynamic responses of helical springs are widely reported as the main reason causing pre-failure in various high-speed conditions. Though the concept of nonlinear springs is proposed to reduce their own dynamic responses, they are found to induce unexpected spike forces during operations. This study presents a dual springs system used within high-speed sports car engines, which aims to mitigate the dynamic responses and spike forces. Analytical models are first developed to calculate the fundamental frequencies of the outer and the inner springs of the system. Then, a transient finite element (FE) model is developed to accurately simulate the dual springs system working at various high engine speeds and validated experimentally by the results of the engine head tests. The simulations reveal that the use of dual springs with different natural frequencies can mitigate the dynamic responses of the whole system to a certain extent. Nevertheless, it is still a compromise as coil clash occurs on each isolated spring though the effects are reduced. The findings of this study indicate that the establishment of direct connections between every component spring would be a promising way to better mitigate the dynamic responses including the effects of coil clash. [ABSTRACT FROM AUTHOR]

This study utilizes a semi-analytical approach to examine the nonlinear dynamic responses of multilayer functionally graded (MFG) cylindrical shells reinforced by FG spiral stiffeners (FGSSs), which may have symmetric or asymmetric angles, under a thermal condition. It is presumed that the temperature is distributed across the thickness direction. The shell includes three layers: an outer ceramic-rich layer, a middle FG layer, and an inner metal-rich layer. By applying classical shell theory (CST), the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the problem of nonlinear vibrations (NVs) has been addressed. Furthermore, the method of multiple scales (MMSs) is applied to investigate the nonlinear vibrational characteristics of the MFG cylindrical shells reinforced by FGSS, particularly focusing on the 1:2:4 internal resonance and the subharmonic resonance of order 1/2. This study finds that FG spiral stiffeners with symmetric or asymmetric angles and ambient temperature significantly affect the vibrational properties of the MFG cylindrical shells reinforced by spiral stiffeners. [ABSTRACT FROM AUTHOR]

This study investigates vibrations of the laminated composite beam (LCB) subjected to axial load and settled on Winkler–Pasternak elastic foundation. The beam model is of Euler–Bernoulli type with cubic order nonlinear elastic load. Two different boundary conditions are considered: (i) Simply Supported (S–S) and (ii) Clamped–Clamped (C–C) ones. Mathematical model of the asymmetric LCB is a partial differential equation. Applying Galerkin procedure, the model is converted into a strong nonlinear ordinary equation. In the paper, the new analytical method, dubbed as the Max–Min Approach (MMA), is adopted to provide more accurate nonlinear analysis of beams. The analytical solution is inferred to investigate the effects of axial force and essential elasticity parameters of foundation on the nonlinear response of the beams. Analytical results are compared with numerical solutions and show good agreement. In addition, the results are compared with previously published ones. It is concluded that MMA used in LCB gives more accurate results than the previously used analytic methods and is practical applicable. The method can be easily extended to high nonlinear vibration problems in LCB under different boundary conditions. [ABSTRACT FROM AUTHOR]

In producing small-scale structures, having nonuniform geometrics and voids as the generation defect is the inevitable problem. However, in the mathematical simulations, the researchers have been more attentive to the perfect and uniform structures because of simple modeling. This article investigates the nonlinear free vibrational behavior of truncated conical imperfect functionally graded (FG) micro-scale tubes, including the porosity, including the various cross-section functions. The modified couple stress theory and Euler-Bernoulli beam theory coupled with the nonlinear Von-Kármán theory are employed based on Hamilton's principles to derive the general equation of motion and related boundary conditions. The cross-section is assumed on the basis of four different functions, involving the uniform section, linear section, convex section, and exponential section. The temperature-dependent materials were combined by ceramic and metal phases along the tube radius that this combination made a functionally graded tube. Furthermore, the nonlinear derived equations are finally solved via the generalized differential quadrature method (GDQM) as the numerical approach coupled with the iteration technique. Since thermal fins, fluid flow diffuser, fluid flow nozzle, etc., are designed for specific purposes with the non-uniform cross-section, the presented results have an excellent sight of developing and designing macro/- and micro-electromechanical systems (MEMS). [ABSTRACT FROM AUTHOR]

This paper examines the nonlinear forced vibrational behaviors of axially functionally graded (AFG) cylindrical microscale tubes under external dynamic stress, including the imperfect porosity. Using the Hamilton principle, the first-order shear deformation beam theory is linked with the modified couple stress theory (MCST) and the nonlinear von-Kármán theory to get the nonlinear governing equations and associated boundary conditions. For cross-sections that vary throughout the tube length, both uniform and non-uniform functions involving the three kinds are assumed. Furthermore, the microtube is constructed of functionally graded materials that vary smoothly throughout the tube length, and the porosity distribution is in the radial direction, resulting in two-dimensional functionally graded (2D-FG) structures with both porosity and material distributions. The nonlinear results are obtained after solving the linear motion equations using the generalized differential quadrature technique (GDQM) and the iteration approach. Finally, the effects of several factors on the natural and resonance frequencies are investigated, including the cross-section, FG parameter, porosity parameter, amplitude, external excitation frequency, and small-scale effect. [ABSTRACT FROM AUTHOR]

The importance of nanoscale devices is increasing day by day. Therefore, nanobeams, nanoplates, nanorods have been the focus of engineers in nanoelectromechanical structures. From that point of view, the nonlinear behaviour of three supported nanobeams is investigated in this paper numerically. Firstly, linear natural frequencies were calculated; and then, nonlinear natural frequencies were found thanks to nonlinear correction terms. Nonlinear natural frequencies versus amplitude and nonlinear frequency response curves are plotted to clarify the nonlinear behaviour. Nonlocal parameters, second support position and different modes effects are examined comprehensively. In addition, the different first and last support types are investigated. It is shown that nonlocal parameters and second support position have great importance for nanobeam. The glorious effect is obtained highest modes. [ABSTRACT FROM AUTHOR]

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Rotating systems are essential components and play a critical role in many industrial sectors. Unbalance is a very common and serious fault that can cause machine downtime, unplanned maintenance, and potential damage to vital rotating machines. Accurately estimating unbalance in rotor–bearing systems is crucial for ensuring the reliable and efficient operation of machinery. This research paper presents a novel approach utilizing artificial neural networks (ANNs) to estimate the unbalance masses in a multidisk system based on simulation data from a nonlinear rotor–bearing system. Additionally, this study explores the effect of various operating parameters on oil film stability and vibration response through a combination of bifurcation diagrams, spectrum cascades, Poincare maps, and orbit and FFT plots. This study demonstrates the effectiveness of ANNs for unbalance estimation in a fast and accurate way and discusses the potential of ANNs in smart online condition monitoring systems. [ABSTRACT FROM AUTHOR]

The operation of an aero-engine involves various non-stationary processes of acceleration and deceleration, with rotational speed varying in response to changing working conditions to meet different power requirements. To investigate the nonlinear dynamic behaviour of cracked blades under variable rotational speed conditions, this study constructed a rotating blade model with edge-penetrating cracks and proposes a component modal synthesis method that accounts for time-varying rotational speed. The nonlinear response behaviours of cracked blades were examined under three distinct operating conditions: spinless, steady speed, and non-constant speed. The findings indicated a competitive relationship between the effects of rotational speed fluctuations and unbalanced excitation on crack nonlinearity. Variations in rotational speed dominated when rotational speed perturbation was minimal; conversely, aerodynamic forces dominated when the effects of rotational speed were pronounced. An increase in rotational speed perturbation enhanced the super-harmonic nonlinearity induced by cracks, elevated the nonlinear damage index (NDI), and accentuated the crack breathing effect. As the perturbation coefficient increased, the super-harmonic nonlinearity of the crack intensified, resulting in a more complex vibration form and phase diagram. [ABSTRACT FROM AUTHOR]

A nondestructive testing method based on nonlinear vibration is usually implemented by measuring the intensity of the second harmonic signal. However, such intensity is much lower than that of the fundamental frequency signal. Particularly, without the help of sufficiently sensitive damage indication effect, the second harmonic signal from the small crack damage can be difficult to identify. In this study, locally resonant metamaterial is introduced into the nonlinear vibration-based nondestructive testing, in order to regulate the second harmonic intensity for a sensitive crack detection. First, an analytical model consisting of a mass-spring chain system and added interior local resonators is studied where a nonlinear bilinear stiffness spring is introduce to the chain system to simulate the breathing crack damage. Then, the incremental harmonic balance method is applied to the model to calculate its harmonic response. It is found that the damage-generated nonlinearity can be effectively regulated in a specific excitation frequency range, where the second harmonic intensity is enhanced apparently by the added local resonators. Moreover, analysis on the frequency-space distribution characteristics of the nonlinear signal reveals a special localization phenomenon. A new damage index is then defined to locate the small breathing crack. Finally, numerical verification on a locally resonant rod with damage, i.e. on a continuous system, has been conducted as the extension of the discrete model examined previously. This research can be a good foundation for metamaterial-promoted vibration-based nondestructive testing. [ABSTRACT FROM AUTHOR]

AbstractThis research examines the nonlinear vibrations and dynamic postbuckling (DPB) analyses of sandwich porous functionally graded (SPFG) cylindrical shells with dual-layered FG porous (FGP) cores exposed to external excitation, using a semi-analytical method. The study investigates two types of FG layers: one with evenly distributed porosities (FG-EPD) and another with unevenly distributed porosities (FG-UEPD). It also studies the FGP cores in four configurations: one featuring symmetric porosity distribution with stiffening in the surface areas (SPD-Stiff), another with softening in the surface areas (SPD-Soft), a third with nonsymmetric porosity distribution (NSPD), and a fourth with uniform porosity distribution (UPD). Therefore, the SPFG cylindrical shells with dual-layered FGP cores with eight different configurations are investigated. Utilizing the classical shell theory (CST) alongside the geometrical nonlinearity in von Kármán–Donnell framework, and Galerkin’s method, this study addresses the nonlinear dynamic problem. An approximate solution for the deflection shape using three terms is selected, and the relationship between frequency and amplitude in nonlinear vibration is clearly defined. The nonlinear dynamic behaviors including vibration and DPB responses are examined using the P-T method, which is named for its use of the piecewise constant argument in conjunction with the Taylor series expansion. The critical dynamic buckling load of SPFG cylindrical shells with dual-layered FGP cores is investigated via the Budiansky–Roth criterion. [ABSTRACT FROM AUTHOR]

Due to installation errors and poor lubrication conditions, the gear system has both eccentricity and wear fault. The eccentricity effect of the gear affects the contact area of the tooth surface, which in turn influences the wear state of the tooth surface. Therefore, it is necessary to study coupling effect of eccentricity and wear fault. A new dynamic model and an improved load tooth contact analysis (LTCA) method are proposed in this paper, both of which can consider the coupling effects of eccentricity and wear fault. The time-varying meshing stiffness (TVMS), tooth contact stress, and wear depth of the gear under eccentricity and wear fault are studied. Finally, the vibration mechanism and spectrum characteristics under speed, eccentricity error, and wear degree are analyzed. Under the coupling effects of eccentricity error and wear fault, the time varying meshing stiffness has a fluctuation period, which is the product of the meshing period and the number of teeth of the eccentric gear. To a certain extent, wear reduce the impact effect caused by eccentricity. The increase of eccentricity error leads to an increase in frequency component on the modulation side. The results provide support for the wear resistance design of gear and the basis for the fault diagnosis of gear-rotor system. [ABSTRACT FROM AUTHOR]

The nonlinear mechanical oscillator with X-shaped-spring suspension has attracted relevant attention in the past couple of years due to its ability to tailor the corresponding stiffness characteristic on purpose and fit diverse engineering needs. This paper deeply investigates the conditions for such a configuration to exhibit a quasi-zero stiffness behaviour with both the linear and cubic elastic term of the force-displacement curve equal to zero. The resulting quintic characteristic leads to a vibration isolator with a much larger isolation frequency band respect to the classical isolator with non-zero cubic elastic term only. A systematic comparison between the quintic and cubic characteristics is performed, emphasizing the asymptotic trends, and thus showing the fundamental behaviours. It is found that the critical damping for an unbounded response of the quintic isolator is proportional to the square of the normalized excitation amplitude, while that of the cubic isolator is directly proportional to the normalized displacement amplitude. This makes the critical damping of the quintic isolator much lower, and thus more favourable in practical engineering applications, where the values of the normalized excitation amplitude are less than one. [ABSTRACT FROM AUTHOR]

In this paper, a FE formulation for nonlinear vibration of fully geometrically exact Timoshenko beams is derived. Firstly, the strong form of the governing equation of motion is obtained without any approximation. Next, the weak relations are used to derive the FE formulation. To obtain the vibration response, a direct integration method is employed to solve highly nonlinear formulation for geometrically exact beams. Finally, some examples are investigated, and very good results with analytical solutions available in the literature are achieved. The results show that the formulation presented in this paper can predict the vibration response of the Timoshenko beam with high accuracy. Moreover, investigating the effect of parameters shows that increasing the length parameter leads to increasing natural frequencies. Besides, the frequency value increases when the amplitude of vibration increases. Furthermore, adding an axial spring can lead to asymptotic behavior in vibration response of the fully exact Timoshenko beams. [ABSTRACT FROM AUTHOR]

AbstractIn this study, the nonlinear forced vibration of graphene/piezoelectric sandwich nanosheets under mechanical impact was investigated. For the first time, linear (displacement and velocity) and nonlinear (displacement) time-delay proportional derivative (PD) controllers were applied to graphene/piezoelectric sandwich nanosheets, and the primary/secondary resonance under different time-delay parameters were analyzed. An approximate analytical solution for the nonlinear forced vibration control equation was obtained using the multiple scale perturbation method, and the stability of graphene/piezoelectric sandwich nanosheets under primary/secondary resonance conditions was discussed using the Ross Herwitz theorem. Finally, the results of this study were compared with those of other studies. The feasibility of the research methodology was demonstrated. On this basis, the research results indicate that linear displacement delay, nonlinear displacement delay, and velocity delay parameters can suppress the unsteady vibration characteristics of the main system. And comparing the linear and nonlinear displacement time-delay, it is found that the nonlinear displacement time-delay has a greater effect on the system. Specifically, the presence of nonlinear displacement time-delay changes the vibration characteristics of the curve from hard spring characteristics to soft spring characteristics. Comparison of displacement time-delay and velocity time-delay reveals that velocity time-delay gives better control over the system. In addition, the results show that the excitation amplitude, nonlocal parameters, and external voltage enhance the nonlinear characteristics of the system under the main and superharmonic resonance conditions before the time-delay control. Subharmonic resonance conditions, the system parameters make the vibration range wider. After the time-delay control, the influence of these three factors on the system vibration is significantly reduced for the three resonance conditions, especially for the non-local parameters. The results of the study can provide guidance for active control of time delay in different types of nanodevices for engineering applications. [ABSTRACT FROM AUTHOR]

Considering the displacement-dependent characteristics of the clamp, a general nonlinear semi-analytical modeling method for the spatial pipeline with arbitrary shapes supported by multiple clamps is proposed to study the vibration characteristics of the pipeline-clamp system. The coupling of the complex spatial pipeline is realized by introducing the connecting springs at the connection region of the straight pipe and curved pipe. The equation of motion for spatial pipeline structure is established based on the Lagrange energy equation and Timoshenko beam theory. High-order polynomials are used to characterize the stiffness and damping characteristics of the clamp, and the simple straight pipe is used as the basic model to reverse the clamp parameters. The influence of clamps on pipeline vibration is skillfully introduced into the nonlinear dynamic model of the spatial pipeline. According to the Newton-Raphson method, the nonlinear equation of motion is solved. Taking the spatial pipeline supported by double clamps as an example, the related experiment tests and ANSYS simulation are carried out, and the effectiveness of the established model is verified by comparing the results. Finally, the nonlinear vibration mechanism of the pipeline-clamp system is analyzed. The modeling method proposed in this paper can provide positive guidance for modeling and vibration analysis of the aero-engine pipeline with arbitrary shapes. [ABSTRACT FROM AUTHOR]

Assembly errors can lead to the eccentricity of rotors, further resulting in angular misalignment of rotors and inducing some secondary misalignments, such as the angular misalignment of gears and tilt misalignment of the inner ring of bearings (TMIRB). Ultimately, these misalignments can lead to rubbing faults. However, these misalignments have not raised significant concern, this article investigates their influence on the vibration responses of a dual-rotor-gear-bearing system with rubbing. First, a finite element model (FEM) of the system is built by using an in-house beam element code, and the nonlinear force model of the bearing is established based on the Hertz contact theory. Then, a new model to simulate angular misalignment of gears is proposed by changing the time-varying meshing stiffness (TVMS). Furthermore, the nonlinear dynamic characteristics of the system are investigated in detail under different misalignment angles and rotating speeds, and some interesting conclusions are summarized as follows. Specifically, analyses of the spectrum cascade of radial and axial responses reveal the presence of rich multi-time frequencies and combined frequencies. Moreover, as the misalignment angle increases, the system experiences partial rubbing, the rotating speed threshold (RST) corresponding to initial rubbing decreases, and the mesh stiffness of gears decreases. In summary, the proposed model and the results of the analysis offer valuable insights into the vibration characteristics of such systems and these findings can be instrumental in optimizing their design and operation. [ABSTRACT FROM AUTHOR]

Dynamic and vibrational behavior of nonlinear resonant pressure micro sensors is studied in this paper using a proposed dynamic model. The basic part of the device is a microplate deflects due to external pressure in presence of electrostatic actuation. The frequency changes because of the microplate deformation is used to estimate the external pressure. For modeling of the micro sensor, the nonlinear governing equation of size dependent microplate in polar coordinate system and based on the modified couple stress theory is presented. Assuming specified number of Taylor expansion terms for electrostatic force, the linear and nonlinear ODE is obtained and nonlinear equation is solved both with multiple time scales method (MTS) and finite difference numerical method. Results indicate that considering finite terms of Taylor expansion (1 term for linear and three terms for MTS method) is the source of error in estimation of pressure or system stability. Using sufficient terms of Taylor Expansion, the error in linear and MTS solutions is vanished. Therefore, the limited values of microplate vibrational amplitude is extracted to increase the accuracy of the sensor in linear action. The effect of size dependency, applied voltage on nonlinear behavior and linearization error is also studied. [ABSTRACT FROM AUTHOR]

This article studied a general analytical method for dynamical behaviors of various FG-GPLRC non-rectangular plates with a piezoelectric layer. For the first time, classical plate theory and Galerkin's method are used to scrutinize the nonlinear vibration of plates with many different shapes. Profiles of new plates are defined by four edges, specifically two parallel opposite edges, and others are assumed to horizontal change according to arbitrary functions. Linear and nonlinear vibration of plates are confirmed with results obtained by Finite Element Method. Effects of environment, material, and geometrical parameters are studied. Besides, periodic and chaotic motions of plates are investigated. [ABSTRACT FROM AUTHOR]

• A new modeling approach for compressor blades is proposed by the Timoshenko beam theory. • The dynamic model of cracked blades is proposed considering the stiffness nonlinearity induced by breathing cracks. • The modeling method is verified by experiments and the proposed dynamic model is validated using ANSYS software. Aero-engine blades may crack under harsh operating environments. This reduces the reliability of the aero-engine and causes catastrophic accidents. Although dynamic modeling and vibration characteristics of simplified blades with cracks have been analyzed extensively, there are few studies on the actual compressor blade with varying sections and twisted shapes. Based on Timoshenko beam theory, a new modeling approach for the compressor blade is proposed. Next, according to the strain energy release rate and Castingliano theory, the dynamic model of cracked compressor blades is established considering the stiffness nonlinearity induced by the breathing crack. The modeling approach is validated by the measured natural frequencies of an intact blade. Then, the dynamic model of the cracked blade is verified by comparing the modal characteristics and vibration characteristics using ANSYS software. Finally, some results show that the natural frequencies f n1 , f n2 , and f n4 increase as the pre-twisted angle and stagger angle increase. Due to the breathing effect, some integer frequencies appear in the spectrum including 0 f e and 2 f e , and the variations in the amplitude of frequencies 0 f r and 2 f r are monotonic under different aerodynamic amplitudes. The research can provide some help for the modeling of the actual blade and fault diagnosis of cracked blades. [ABSTRACT FROM AUTHOR]

Abstract This research explores the efficacy of integrating nonlinear single-degree-of-freedom systems in the vibration control of rod coupling systems. By interlinking two rods with a nonlinear single-degree-of-freedom system as the intermediary, the study employs the Lagrange method (LM) to forecast nonlinear vibrational behaviors. The findings, substantiated by numerical analyses, affirm the precision of LM in gauging the amplitude responses when such a nonlinear system is utilized. The nonlinear dynamics, characterized by intricate vibrational patterns, peak jumping phenomena, and the migration of resonance zones, are induced by the nonlinear single-degree-of-freedom system. By fine-tuning the system’s parameters, significant alterations in the vibrational states of the rod coupling system are achievable. This suggests that the application of a nonlinear single-degree-of-freedom system is a viable strategy for modulating vibrations in rod systems. Furthermore, optimal parameterization of this system is proven to effectively dampen vibrations, showcasing its potential as a sophisticated mechanism for vibration suppression in coupled rod configurations.

Abstract A new control approach based on fuzzy sliding mode control (FSMC) is proposed to regulate the chaotic vibration of an axial string. Hamilton’s principle is used to formulate the nonlinear equation of motion of the axial translation string, and the von Kármán equations are used to analyse the geometric nonlinearity. The governing equations are nondimensionalized as partial differential equations and transformed into a nonlinear 3-dimensional system via the third-order Galerkin approach. An active control technique based on the FSMC approach is suggested for the derived dynamic system. By using a recurrent neural network model, we can accurately predict and effectively apply a control strategy to suppress chaotic movements. The necessity of the suggested active control method in the regulation of the nonlinear axial translation string system is proven using different chaotic vibrations. The results show that the study of the chaotic vibrations of axially translating strings requires nonlinear multidimensional dynamic systems of axially moving strings; the validity of the proposed control strategy in controlling the chaotic vibration of axially moving strings in a multidimensional form is demonstrated.

The primary focus of this study is to analyze the nonlinear vibration patterns and parametric excitation of embedded Euler–Bernoulli nanobeams subjected to thermo-magneto-mechanical loads. The Euler–Bernoulli nanobeam is developed with external parametric excitation. By utilizing nonlocal continuum theory and nonlinear von Karman beam theory, the governing equation of motion is derived. Subsequently, the homotopy perturbation technique is employed to determine the vibration frequencies. Finally, the modulation equation of Euler–Bernoulli nanobeams is derived for simply supported boundary conditions. The impacts of magnetic potential, temperature, damping coefficient, Winkler coefficient, and nonlocal parameters are tested numerically on nonlinear frequency–amplitude and parametric excitation–amplitude responses. Results demonstrate that physical variables significantly influence both nonlinear frequency behavior and parametric excitation.

During the bearing operation, surface waviness can cause severe nonlinear vibrations and reduce the life and reliability of bearing-rotor systems. A temperature increase can deform the surface waviness, which can exacerbate this unstable vibration. To address this problem, a dynamic waviness model considering thermal deformation is proposed, and the dynamic support stiffness is calculated and introduced into the dynamic model of a 12-DOF full-ceramic bearing-rotor system. The Newton–Raphson and Newmark-β nested iterative solution method combines the quasi-static and dynamical models. The bifurcation, maximum Lyapunov exponent, and Poincaré mapping analysis methods serve to analyse how thermal deformation, waviness amplitude and other parameters affect the system nonlinear vibration. Experimental measurements are conducted to verify the model accuracy and reveal that a larger waviness amplitude causes a delayed motion state and expands the influence of the thermal deformation. The wavenumber is close to an integer multiple of the ball, and the time-varying displacement excitation curve shows a monotonic variation trend, which makes the system violently vibrate. The model effectively reveals the characteristics of the failure frequency and provides important theoretical support for the fault detection of full-ceramic bearings. [ABSTRACT FROM AUTHOR]

The vibration character of piezoelectric semiconductor nano-plate is important for understanding the multi-fields coupling and optimizing the serving behavior. In this article, the nonlinear vibration of five-layered functionally graded piezoelectric semiconductor nano-plate based on Pasternak foundation is studied, and the nonlocal theory is used to analyze the size-dependent dynamic response of nano-plate. Combining the Von karman's nonlinear deformation theory and the constitutive of piezoelectric semiconductor layers, Hamilton's principle is introduced to derive the nonlinear governing equations. To solve the nonlinear governing equations, the updated iteration method for this problem is proposed. Through numerical examples, it is found that the initial electron concentration in piezoelectric semiconductor layer, the nonlocal parameter, the functionally graded index in the plate, the elastic modulus of Pasternak foundation and the geometrical parameters can be designed to effectively tune the dynamic nonlinear frequency and damping of layered functionally graded piezoelectric semiconductor nanoplate. The interaction of these parameters is also analyzed in detail. Comparison with existing numerical results is also presented. A new way is provided to tune the nonlinear vibration of multi-layered piezoelectric semiconductor nano-plate. [ABSTRACT FROM AUTHOR]

This article investigates the non-linear forced vibrations and primary resonance analysis of stiffened FGM conical panels (OCPs) resting on a viscoelastic foundation utilizing a semi-analytical method. The classical shells theory and von Kármán nonlinear strain–displacement relations are used to model of OCPs. The equations of motion are derived by applying Hamilton's principle. Then, the dimensionless equations of motion are established and converted into dimensionless nonlinear ordinary differential equations by applying Galerkin's method. The solution of the ordinary differential equations is carried out based on the multiple-scale method for analyzing the vibration behavior. In this regard, the necessary relations for the nonlinear primary resonance and internal resonance of stiffened FGM-OCPs are obtained. To validate the suggested methodology, first, the results are verified with various previous research. Second, a numerical method based on the fourth-order Runge-Kutta's approach is used for verifying the nonlinear vibration analysis. Finally, changes in various parameters such as viscoelastic foundation coefficients, stiffeners, temperature, semi-vertex angle and subtended angle are examined by helping the frequency response plots. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the combined influences of pore imperfection, initial geometric imperfection, elasticity of tangential constraints of ends, elastic foundations and elevated temperature on the nonlinear vibration of functionally graded material (FGM) beams. The pores are assumed to distribute into FGM according to even and uneven patterns and effective properties of porous FGM are estimated using a modified rule of mixture. Motion equations of geometrically imperfect beams are established within the framework of Timoshenko beam theory incorporating von Kármán nonlinearity and foundation interaction. Analytical solutions are assumed to satisfy simply supported and clamped conditions of beam ends and Galerkin method is applied to derive a nonlinear time ordinary differential equation. The frequencies of nonlinear free vibration are determined employing fourth-order Runge-Kutta numerical integration scheme. Parametric studies are carried out to assess numerous effects on both linear and nonlinear frequencies. The results reveal that frequency nonlinearity is more significant for beams with tangentially restrained ends, especially at elevated temperatures. It is also found that geometric imperfection increases the linear frequency and lowers ratio of nonlinear-to-linear frequencies. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear vibrational characteristics of the two-dimensional temperature-dependent, and imperfect functionally graded (2D-FG) truncated conical nanotubes based on the nonlocal strain gradient theory coupled with Von-Kármán nonlinear theory using a novel high-order tube theory along with the first-order beam theory. The Hamilton principle is used to derive the nonlinear and nonlocal governing equations and associated boundary conditions. A numerical approach, including a couple of iteration techniques and the generalized differential quadrature method (GDQM), is used to solve linear and nonlinear equations for different clamped and simply-supported boundary conditions. A composition makes the functionally graded temperature/- and porosity-dependent material of ceramic and metal phases in the radius direction that the tube radius also changes along the tube length, which means the properties of the material are varied in both axial and radial direction that means it is two-dimensional functionally graded material (2D-FGM). The obtained results are discussed in detail to investigate the effect of the nonlocal and strain gradient parameter, temperature change, nonlinear amplitude, porosity parameter, radius aspect ratio, etc., on the vibrational behavior of nanotubes. [ABSTRACT FROM AUTHOR]

Abstract In deep‐ocean natural gas hydrate exploitation operation, the fatigue failure mechanism has attracted more and more attention from scholars, but it has not been effectively disclosed. Therefore, in this work, a multifield coupling and multiple‐nonlinear vibration model of lifting pipe is established, which can accurately determine the alternating stress of deep‐ocean lifting pipe. Second, according to Forman theory, the calculation method of crack propagation length and depth on the surface of a deep‐water riser is established, which is verified by the comparison between the experimental and theoretical model calculation results. The results demonstrate that, first, the effect of residual stress in the welded joint of deep‐ocean lifting pipe should be considered in the later parameter influence analysis. Second, the fatigue growth life of deep‐water pipe with small outflow velocity is mainly determined by tensile stress, and that is determined by both tensile stress and bending stress with large outflow velocity. Third, more attention should be paid to the vibration of the lower pipe on‐site to reduce its vibration frequency and vibration stress amplitude, which can effectively reduce the surface crack propagation state of the deep‐ocean pipe and improve the service life of the pipe. Fourth, properly adjusting the tension coefficient of the tensioner during field operation can effectively improve the safety of the pipe, and the optimal tension coefficient is related to the configuration of the deep‐ocean pipe system, which can be analyzed and determined by the model.

Abstract This research introduces a methodology for data-driven regression modeling of components exhibiting nonlinear characteristics, utilizing the sparse identification of nonlinear dynamics (SINDy) method. The SINDy method is extended to formulate regression models for interconnecting components with nonlinear traits, yielding governing equations with physically interpretable solutions. The proposed methodology focuses on extracting a model that balances accuracy and sparsity among various regression models. In this process, a comprehensive model was generated using linear term weights and an error histogram. The applicability of the proposed approach is demonstrated through a case study involving a sponge gasket with nonlinear characteristics. By contrasting the predictive model with experimental responses, the reliability of the methodology is verified. The results highlight that the regression model, based on the proposed technique, can effectively establish an accurate dynamical system model, accounting for realistic conditions.

The nonlinear vibrations of composite cylindrical–cylindrical shells with bolt loosening connections are investigated. First, a theoretical model of such a combined shell is developed, with a multisegmental virtual material ring technique being adopted to replicate the partial bolt looseness in the bolted connection zone of two single shells. Furthermore, to consider the nonlinear vibration issue of such a bolted connection zone affected by external excitation amplitude, the equivalent Young’s modulus of the virtual material is defined, and the equation of motion is derived to solve nonlinear vibration parameters. Finally, three single composite cylindrical shells are connected with 12 bolts to form two combined shell specimens, and experimental tests are carried out to validate the model and examine the nonlinear vibration characteristics of such combined shells. Also, the impact of partial bolt loosening parameters on the nonlinear vibration behaviors is investigated with some important findings being summarized. The analysis methods, modeling techniques, test methods and important conclusions proposed in this study provide a useful reference for the study of the vibration issues of bolted composite shells. [ABSTRACT FROM AUTHOR]

Studying the electromechanical response behavior of piezoelectric thin films under different loading conditions is of great value for the development and optimization of piezoelectric sensors and flexible portable electronic devices. This paper establishes the theory of large deflection vibration of rectangular four-edge simply supported piezoelectric thin films using the energy method, and analyzes the electromechanical response characteristics of vibration force (including resonant frequency and nonlinear vibration). Meanwhile, the electromechanical response behavior of Poly(vinylidene fluoride) (PVDF) films under different loading conditions (static and harmonic vibration) is analyzed. The study investigates the nonlinear vibration characteristics and resonance frequency variations under different film sizes and thickness conditions in the case of various loading conditions. The developed model can predict the resonance frequency associated with the plate dimensions. This study is of great significance for the research and application of laminated piezoelectric film sensors. [ABSTRACT FROM AUTHOR]

In this research, the nonlinear vibration behavior of axially functionally graded (AFG) nano-scale truncated conical tubes (with non-uniform cross-section), including the porosity, is presented for the first time based on the Euler-Bernoulli beam theory and the von-Kármán's nonlinear strain-displacement and nonlinear nonlocal boundary conditions. The effect of being at the tapered nanosize model is supposedly based on the nonlocal strain gradient theory using the Hamilton principle to extract the equation of motions and nonlinear time-dependent nonlocal boundary conditions. The material properties and thickness of nano-tube are varying along the length of tubes. The generalized differential quadrature method (GDQM) is utilized with the iteration method to solve the complicated nonlinear equations. The numerical results in tabular and graphical styles present for various nonlinear amplitudes, the AFG power indexes, the rate of the cross-section change, the porosity parameter, and the nonlocal gradient strain parameter for both simply supported, fully clamped, and simply supported-clamped boundary conditions in detail. [ABSTRACT FROM AUTHOR]

This paper deals with the free and forced, linear and nonlinear vibration of functionally graded (along with thickness) nanotube, considering the non-uniform cross-section that made a two-dimensional functionally graded (2D-FG) structure. The bi-dimensional nanostructure-dependent governing equation is modeled based on the classic beam theory (Euler-Bernoulli), and they are derived by Hamilton's principle based on nonlocal gradient strain theory considering the von-Kármán nonlinear strain and the external harmonic load. To solve the general equations and calculate the results, the generalized differential quadrature method (GDQM) was used coupled with the numerical iteration method for the nonlinear response. The results are discussed for the different simply-supported and clamped boundary conditions. The 2D-FG nanotube's behavior is analyzed for different nonlinear amplitudes, nonlocal strain gradient parameters and nonlocal parameters, different rates of cross-sections, and different material distributions. [ABSTRACT FROM AUTHOR]

Spinning joined conical-cylindrical shells (JCCSs) with bolt boundary constraints are widely used in rotor systems of aero-engines, and always operate in thermal environments. Under external excitation, the friction hysteresis phenomenon of bolt connections often occurs, and the high-temperature environment further changes the friction characteristics of the connection interface, making the vibration characteristics of the system nonlinear and complex. Till now, research on the nonlinear vibration of spinning JCCSs caused by bolt connections with the temperature effect is scarce. To address this problem, this study develops a nonlinear dynamic model of spinning JCCSs with bolt boundary constraints in a thermal environment for the first time. A novel equivalent mechanical model of the bolt connection is established, which is represented by the nonlinear stiffness and damping with amplitude and temperature-dependent characteristics. The energy expressions of spinning conical and cylindrical shell components are deduced by Donnell's shell theory. The rigid joint between the conical and cylindrical shells is realized via successive distributed artificial springs. The Chebyshev polynomials are adopted as the admissible functions, and the governing equation is obtained by the Lagrange equation. Then, by comparison with the available literature, finite element simulation, and experiment test, the accuracy of the established theoretical model is validated. The nonlinear vibration mechanism is illustrated from aspects of equivalent stiffness and equivalent damping. Finally, the effects of spinning speed and temperature on nonlinear vibrations of bolted JCCSs are further investigated. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the nonlinear vibration characteristics and stability of a dual-disk rotor-bearing system under multi-frequency excitations. A 4-degree-of-freedom dynamic model is established using the assumed mode method, considering the bearing's cubic nonlinearity. The system is solved using the multiple scale method combined with arc-length continuation. The stability of the system's solutions is determined by solving the eigenvalues of the Jacobian matrix of the averaged equations. The nonlinear vibration characteristics and stability of the dual-disk rotor system under simultaneous resonance conditions are obtained. The results show that changes in system parameters can lead to Saddle-Node and Hopf bifurcations, as well as the occurrence of multi-valued solutions and symmetry-breaking phenomena. Additionally, simultaneous resonance leads to interaction between the two modes, where the relative positions of the resonance peaks of these modes influence the system's dynamic behavior. Variations in system parameters can alter the relative positions of resonance peaks, leading to more complex effects on nonlinear responses. This research provides significant insights into the dynamic behavior of the dual-disk rotor-bearing system under multi-frequency excitations, which is meaningful for designing and optimizing rotor systems. [ABSTRACT FROM AUTHOR]