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AbstractIn this study, using an analytical and precise solution, the dynamic transverse deflection of a five-layer beam with Prussian core with graphene platelet reinforced composite (GPLRC) under a moving harmonic load on a Pasternak elastic substrate is analyzed. First, the properties of the porous core materials and the piezoelectric layer and surface, which were graphene platelet reinforcements (GPLRs), were defined. The constitutive relations were extended using the Bonilla’s higher-order theory and Hamilton’s principle, relationships were extracted. Finally, using the Laplace method and analytical solution. A parametric analysis is provided to investigate impact of temperature distribution, porosity coefficient, thickness ratio, spring constant, voltage and excitation frequency on the responses. [ABSTRACT FROM AUTHOR]

This paper introduces a unified and exact method for the vibration solution of three versions of Timoshenko beam theory, namely the classical Timoshenko beam theory (TBT), truncated Timoshenko beam theory (T-TBT), and slope inertia Timoshenko beam theory (S-TBT). The proposed unified method enables the free vibration analysis of these three beam theories performed by only one equation, which avoids separate modeling and solution with different beam theories. Firstly, the comparison of three beam theories is conducted with a special focus on deriving the governing differential equation of T-TBT based on Hamilton's principle. Then, two parameters are introduced to unify the three governing differential equations. The dynamic stiffness matrix is derived in a unified form by reducing the order of inverse matrix operation from 2 n to n, allowing the dynamic properties of three beam theories to be characterized with only a single model. Additionally, this paper also derives the unified frequency-dependent mass and stiffness matrices based on the unified dynamic stiffness matrix, which eliminates the limitation of DSM in studying the independent influence of the structure's mass and stiffness characteristics. Finally, the discrepancies of the three beam theories are discussed under different boundary conditions and aspect ratios. [ABSTRACT FROM AUTHOR]

In order to bridge the gap between the effects of superposition of unequal amplitude waves on superimposed waves, this paper investigates the effects of variable amplitude superimposed waves on piezoelectric actuators. The generation mechanism of traveling waves is explored from the principle of superposition of waves. A mathematical model of the piezoelectric beam is established based on the Euler-Bernoulli beam theory and the Lagrange equation. It is the first time that the effects of variable amplitude superimposed waves on motion performance are investigated from both theoretical and experimental perspectives. The effects of variable amplitude waves on kinematic performance are tested by changing different excitation frequencies, different positions and different loadings. The relationship between the amplitude ratio A and the motion performance is given. It is shown that there is an approximately linear negative correlation between the amplitude ratio and the motion performance when the amplitude ratio A = 1–2.4. This study provides a new idea for the generation of traveling waves and provides a reference for the design and application of piezoelectric actuators. [ABSTRACT FROM AUTHOR]

Anchoring is a highly effective means to reinforce jointed rock masses. In addition to the axial force from the anchor bolt, the effect of its transverse force in constraining the displacement of the structural plane cannot be ignored. Thus, this paper studies the combined action of the axial and shear forces of an anchor bolt on enhancing the shear strength of the anchored joint. In this work, first, laboratory direct shear tests are conducted to study the evolution of the peak shear strength of the anchored joint with increasing angle between the shear direction and bolt inclination. Second, to further verify this trend, numerical simulation with the finite difference method is used to simulate the same direct shear tests to reveal the lateral and axial stresses and deformations of the bolt. Finally, according to classical beam theory, the mechanical analysis model of a bolt subjected to the combined action of axial tension and lateral shear is established, which takes the realistic stress and deformation patterns of the bolt from the numerical simulation into account. The results show that the lateral restraint of the bolt plays a significant role in the shear strength of the anchored joint, its enhancing effect first increases and then decreases with increasing installation angle, and the optimal installation angle providing the maximum shear strength is approximately 60°. In addition, it is concluded that the shear resistance of the bolt is mainly due to its axial force when the installation angle is relatively small; conversely, the shear resistance of the bolt is mainly due to its shear force when the installation angle is relatively large. Highlights: A new approach for calculating the anchoring force considering the combined action of the transverse restraint and axial restraint of the bolt is presented. A calculation method for the optimal anchoring angle is presented, and its value is suggested to be approximately 60° in this study. The contribution rates of the axial force and tangential force to the anchoring force are not equal and vary with the change in the anchoring angle. [ABSTRACT FROM AUTHOR]

Shear waves in underground longitudinal structures impose deformations that need to be accounted for in structural design. Simplified approaches for such structures typically consider the Winkler foundation model, assuming Euler-Bernoulli beam theory, which neglects shearing-induced distortions, especially significant when shear waves are a dominant component of the seismic motion. In order to overcome these limitations, Timoshenko beam models have been proposed in the literature. These approaches however depend on an appropriate determination of the ground springs. Existing analytical formulations often assume plane-strain conditions, inadequate for representing low frequencies and thus are not directly applicable for pseudo-static interaction analyses. The present paper develops analytical solutions to determine transverse and rotation Winkler springs for structures subjected shear waves. The proposed springs overcome the drawbacks of plane-strain models and can be construed as a generalisation of them. The springs are obtained as a function of the seismic wavelength and the ground-structure stiffness contrast. Results obtained are validated against solutions from the literature and numerical results from a full 3D finite-element model. A non-dimensional parametric study is also presented, that allow an expedited evaluation of ground springs for practical applications. [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]

A wavelet based finite element method (WBFEM) using B-spline wavelet on the interval is developed in this paper for modeling multi-span pipes conveying fluid with different support conditions. The pipe element is considered as a beam element which is formulated based on Euler–Bernoulli and Timoshenko beam theories. The generalized eigenvalue problem is formulated and solved to obtain the modal characteristics of the multi-span pipe. In comparison to the conventional finite element method, the developed WBFEM discretization scheme uses appreciably less elements for modeling the multi-span pipe. Numerical solutions are obtained and compared with some available results in the literature and those obtained by ANSYS to verify the accuracy and efficiency of the developed method. [ABSTRACT FROM AUTHOR]

• An orbit-attitude-structure-thermal coupled modelling method is proposed. • A unified-meshes ANCF element for temperature-displacement field is proposed. • Both axial and circumferential heat conduction are considered. • Three quasi-static models are proposed to predict the thermally induced vibration. Large space structures would exhibit orbit-attitude-structure-thermal coupled effects in complicated space environment. Thus, a new thermal-structure coupled modelling method is proposed using gradient-deficient absolute nodal coordinate formulation beam elements. Compared to the previous methods, both axial and circumferential heat conduction are considered. The cubic interpolation in temperature field instead of the linear interpolation is adopted to obtain a unified-mesh temperature-displacement description. The gravitational force and gravity gradient are modelled, and the effects of attitude motion and structural deformation on solar radiation intensity are considered. In addition, three kinds of quasi-static thermal-structure coupled models are proposed based on Euler-Bernoulli beam theory. Based on the quasi-static models, the theoretical formulas are derived to effectively predict the thermally induced vibrations of the beam in space. Four numerical examples are studied to validate the proposed models, including the heat conduction examples with three boundary conditions and a thermal-structure coupled cantilever beam example. Based on the proposed formulation, the orbit-attitude-structure-thermal coupled dynamics of a multibody system consisted of a rigid body and a large flexible appendage is investigated considering the gravity gradient, solar radiation, Earth's shadow, and self-shadow. [ABSTRACT FROM AUTHOR]

• A mathematical model for inverse kinematics and shape modeling of continuum robots is presented. • The inverse kinematics algorithm performs very well in the accuracy and efficiency by simulation. • Shape modeling of continuum robots is verified by prototype experiment. A mathematical model for the inverse kinematics and shape modeling of continuum robots is presented in this paper. This method simplifies the forward kinematics derivation process by introducing a rotation axis. In the inverse kinematics solution, an iterative approach is employed to try different initial values, and the optimal initial value is obtained by computing the condition number of the Jacobian matrix. Simulation experiments are verified that optimized initial values can effectively enhance the efficiency of inverse kinematics solution. Based on the Euler-Bernoulli beam theory, the shape modeling of continuum robots is derived, and the mathematical model of the relationship between robot shape and end loads is established. Finally, the mathematical model is verified through prototype experiments, demonstrating that the established shape modeling can achieve accurate simulation of deformation within a range where the bending angle is less than 90°, with errors within 10 %. [ABSTRACT FROM AUTHOR]

Due to their elemental porosity, porous materials display individual mechanical properties, rendering them essential components in various engineering applications. So, this study investigates the lateral‐torsional buckling (LTB) sensitivity of porous orthotropic rectangular beams subjected to a concentrated load, including the warping effects. Porosity‐dependent material properties vary along the beam's height via four different porosity distribution patterns. The constitutive equations are obtained using the principle of virtual work based on the classical beam theory containing the warping effect, and the governing equations are solved by performing the Ritz method to obtain the critical LTB load. The porous orthotropic beams and the warping effects add complexity to the analysis. So, the influence of some parameters, such as porosity coefficients, porosity distribution patterns, orthotropy, height‐to‐width ratio, slenderness ratio, and warping coefficients, on the LTB characteristics of porous orthotropic rectangular beams are investigated in detail. The novelty of this study lies in its comprehensive LTB analysis of orthotropic rectangular beams under specific effects, such as porosity and warping factors. The findings offer valuable insights into the LTB characteristics of orthotropic porous beams, contributing to an improved comprehension of their structural behavior and facilitating the design of engineering structures. This study contributes to the composite materials and structural stability analysis, offering potential applications in many engineering domains. [ABSTRACT FROM AUTHOR]

Unbalance in rotating machines, caused by manufacturing defects and wear, can induce severe vibrations in base structures. As the rotor accelerates from static to high speeds, multiple frequencies may be excited. To effectively suppress vibrations across all speeds, a bi-stable nonlinear energy sink (BNES) is attached to a cantilever beam with an unbalanced rotor. The dynamic equation of the beam-BNES system is derived using Euler-Bernoulli beam theory and the Euler-Lagrange equation, followed by Galerkin discretization. A Multi-Objective Genetic Algorithm optimizes the BNES parameters. Results indicate that the BNES reduces multiple resonant amplitudes by 80% to 95%. Energy dissipation for the first and second beam modes was 85% and 78%, respectively. The system's bifurcation diagram reveals a stable multi-periodic response across a wide range of unbalance levels. Performance measures show that the NES with an additional linear stiffness element or the BNES surpasses traditional NES. [ABSTRACT FROM AUTHOR]

In the current paper, a new first-order Timoshenko's theory (N-FSDBT) based on the indefinite integral is proposed to examine the vibrational behavior of power-law (P-FG), sigmoid (S-FG), and exponential (E-FG) functionally graded beams. The developed formulation takes into consideration the effect of the transverse shear deformation. During the manufacturing process, faults, such as the presence of micro voids or porosities in FGMs, structural imperfections may arise in the material. For this purpose, this research has focused on the modification of the mixture rules including the porosity volume fraction. To illustrate the porosity variation throughout the body of the structures, the uniform, nonuniform and mass-density porosity distribution are considered in the present examination. Mathematical approach is used to simplify the FG beam governing equation based on classical beam theory (CBT) and new-FSDBT frame works for free vibration. The resultant equations of motion are solved using the Navier's technique, for simply supported FG beams. To validate the results, a parameter study was presented to analyze the impact of the types of volume fraction (FG beam-type), the effects of porosity distribution, material exponent parameter, slenderness ratio, and porosity index on the dynamic behavior of imperfect FG beams. [ABSTRACT FROM AUTHOR]

The thermoelastic coupling between strain and temperature fields arising out from temperature gradient, while bending of an oscillating structure, leads to irreversible heat conduction, which causes energy dissipation in such vibrating systems. The estimation of thermoelastic damping (TED) in micro- and nano-mechanical resonators is a significant aspect of acquiring a high quality factor (Q-factor). Yang et al. [Couple stress based strain gradient theory for elasticity. Int J Solids Struct. 2002;39(10):2731–2743.] developed the modified couple stress theory (MCST) that involves only one material length scale parameter. The present work attempts to investigate TED in micro/nano-beam resonators utilizing MCST and the recently proposed Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. Adopting the frequency approach method, we derive the size-dependent expression of the inverse quality factor for evaluating TED in rectangular micro/nano-beam resonators. Furthermore, the impact of the material length scale parameter on TED associated with MCST for silicon micro-beam resonator is investigated in detail by comparing the present results with those predicted by classical continuum theory (CCT). The obtained results are also compared with the existing results for the Lord–Shulman (LS) and Green–Naghdi (GN-III) thermoelasticity theories. Moreover, the effects of other important parameters like beam thickness, beam length, aspect ratio, phase-lag on TED in the present context are highlighted. [ABSTRACT FROM AUTHOR]

Underwater soft manipulators are increasingly used for grasping underwater organisms and cultural relics due to their compliance and ability to protect delicate objects. Unlike rigid manipulators, these soft manipulators feature underwater soft bending actuators that deform under external forces, making their shape and output force challenging to predict. Consequently, classical beam theory is no longer applicable. To address these issues, this article models the underwater soft bending actuator as a cantilever beam and establishes its shape and output force using elliptic integral functions. Additionally, this article proposes a method for determining the unknown parameters of the driver shape and output force model using optimization techniques and introduces a solution process based on the particle swarm optimization framework. Given the role of tensile and bending stiffness in the actuator's performance, this paper employs a parameter identification method based on length and bending angle information. Tests demonstrate that the proposed method effectively estimates the deformation and output force of the underwater soft bending actuators, confirming its accuracy. [ABSTRACT FROM AUTHOR]

Steel-concrete composite beams are ubiquitous in construction, especially in bridge building. This paper addresses the harvesting of energy from a beam subjected to a moving harmonic load using analytical methods. The harvesting is performed by attaching a thin piezoelectric patch directly to the bottom surface of the steel beam. Based on the assumptions of the Euler-Bernoulli beam theory for the relationship between displacement and deformation, the differential equation for the vibration of a beam is derived using Hamiltonian principles. A theoretical formulation is presented for the problem of harvesting energy from a harmonic moving load on a simply supported beam. The dynamic responses are determined in exact form using analytical methods, and the energy harvested from the piezoelectric material layer is calculated. The influence of the speed of the load on the energy harvesting of the piezoelectric material layer is investigated in detail. [ABSTRACT FROM AUTHOR]

The Acoustic Black Hole (ABH) is an effective structure for harvesting and dissipating energy from flexural waves. It works by reducing the thickness of the ABH wedge in a power law relationship with m ≥ 2, which rapidly decreases the local phase velocity of flexural waves and leads to an energy convergence effect. However, the vibration performance may differ if the tapered wedge does not meet the requirements of a typical ABH. This article introduces and discusses two types of "pseudo-ABH" wedges: linear-degenerate ABH and step-degenerate ABH. These wedges do not follow the power-law and continuity conditions of typical ABH, respectively. To establish the dynamic models of pseudo-ABH wedges, the lumped-mass transfer matrix method (LTMM) and traveling wave analysis are introduced and validated using analytic solutions of the non-uniform one-dimensional Euler-Bernoulli beam and finite element method. Meanwhile, a good match between the results of the Timoshenko and Euler-Bernoulli beam theory also indicates the correctness of our model. The energy ratio and reflection coefficient are defined to characterize the energy accumulation effect and vibration absorption performance of the pseudo-ABH wedges. The vibration performance of the linear-degenerate ABH is closer to the typical ABH than the step-degenerate ABH. The step-degenerate ABH has more effective energy accumulation and reduction performance for individual frequencies. However, as the number of segments in the step-degenerate ABH increases, its dynamic performance becomes closer to that of the typical ABH. The novelty of this article is to study vibration energy accumulation and absorption characteristics of pseudo acoustic black hole wedges using LTMM model, disclose the differences of linear and step degenerate ABH for their performance, and recommend the step degenerate ABH in place of the typical ABH of a power law thickness relationship. [ABSTRACT FROM AUTHOR]

THIS STUDY DEALS WITH THE VIBRATION RESPONSE of porous functionally graded (FG) nanobeams under hygro-thermal loadings. The FG nanobeam model is developed based on the Euler-Bernoulli beam theory, in which the doublet mechanics is implemented to account for the size effect. The material properties of the FG nanobeam are assumed to vary along the thickness direction of the beam according to the power-law form with the temperature dependent and porosity phases. The approximate Ritz method is employed to obtain the natural frequencies of porous FG nanobeam models for various boundary conditions. The influences of several parameters such as temperature rise, moisture concentration, porosity volume fraction, material gradient index, material length scale parameter and mode number on the free vibration response of the porous FG nanobeams under hygro-thermal environments are examined in detail. It is explicitly shown that the proposed approach can provide accurate frequency results of FG nanobeams as compared to existing studies in open literature. These study's results may be useful for the optimal and safety design of nano-electro-mechanical systems. [ABSTRACT FROM AUTHOR]

The operation of wind turbines involves a complex interaction between aerodynamics, structural mechanics, and control systems. However, the control system is frequently overlooked. To investigate the impact of the control system on the aerodynamic characteristics and elastic deformations of wind turbines, this paper initially integrates the control system into the blade element momentum theory (BEMT) for calculating aerodynamic forces. Subsequently, the control system is incorporated into fluid-structure interaction (FSI) calculations to assess its influence on the overall performance of the turbine. The control system employs variable speed and pitch control, while the structural dynamics are modeled using the Euler-Bernoulli beam theory. When the control system is integrated with blade element momentum theory to calculate the aerodynamic forces of the wind rotor, it is observed that, below the rated wind speed, a portion of the torque error is transferred to the rotor speed. In contrast, above the rated wind speed, the entire torque error is transferred to the blade pitch angle (BPA). Crucially, when the control system is integrated, the rotor speed and BPA are no longer treated as known parameters. This approach enables the prediction of aerodynamic characteristics of the wind rotor, particularly under complex wind speed profiles. The control system exerts a significant influence on the FSI results, particularly in the range of wind speeds that correspond to larger blade deformations. This work can provide a reference for the calculation of aerodynamic characteristics and FSI of wind turbines under complex wind conditions. [ABSTRACT FROM AUTHOR]

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This study presents analytical solutions using the finite sine transformation methodology (FSTM) for the natural dynamic solutions of thick beams. The Euler-Bernoulli beam theory (EBBT) disregards the contributions of transverse shear strains due to the Euler-Bernoulli-Navier orthogonality hypothesis used in its formulation and is unsuitable for thick beams. It derived a variational formulation of flexural vibration equations of sinusoidal shear deformable beams using first principles approach. The governing equation is formulated for transverse dynamic loading and in-plane compressive force as a non-homogeneous partial differential equation (PDE). The PDE did not need shear correction factors. The formulation yielded a cosine function shaped transverse shear strain and stress distribution which was maximum at the neutral axis and vanished at the beam surfaces. The PDE was solved for free flexural vibration where it became homogeneous due to the absence of forcing excitation forces. The FSTM was used for solving simply supported beams since sinusoidal kernel complies with end conditions. The problem simplifies for harmonic excitation to an algebraic eigenvalue problem solvable using algebraic methods. The roots are utilized to compute modal vibrations and the resonant vibration frequency at the first mode, (n = 1). The resonant frequencies obtained are identical with past results that used theory of elasticity technique. The results for the first five vibration modes are also close to previous results obtained thick beam models for all modes and aspect ratios considered. The effectiveness of the FSTM and its accuracy has been demonstrated for simply supported thick beam vibration problems. [ABSTRACT FROM AUTHOR]

We study the electrothermal actuation of nanomechanical motion using a combination of numerical simulations and analytical solutions. The nanoelectrothermal actuator structure is a u-shaped gold nanoresistor that is patterned on the anchor of a doubly clamped nanomechanical beam or a microcantilever resonator. This design has been used in recent experiments successfully. In our finite-element analysis (FEA) based model, our input is an ac current; we first calculate the temperature oscillations due to Joule heating using Ohm's law and the heat equation; we then determine the thermally induced bending moment and the displacement profile of the beam by coupling the temperature field to Euler–Bernoulli beam theory with tension. Our model efficiently combines transient and frequency-domain analyses: we compute the temperature field using a transient approach and then impose this temperature field as a harmonic perturbation for determining the mechanical response in the frequency domain. This unique modeling method offers lower computational complexity and improved accuracy and is faster than a fully transient FEA approach. Our dynamical model computes the temperature and displacement fields in the time domain over a broad range of actuation frequencies and amplitudes. We validate the numerical results by directly comparing them with experimentally measured displacement amplitudes of nano-electro-mechanical system beams around their eigenmodes in vacuum. Our model predicts a thermal time constant of 1.9 ns in vacuum for our particular structures, indicating that electrothermal actuation is efficient up to ∼ 80 MHz. We also investigate the thermal response of the actuator when immersed in a variety of fluids. [ABSTRACT FROM AUTHOR]

The unique mechanical properties of graphene have made it a topic of enormous research interest over the last few years. Studying graphene's pull-in instability is key for its application in nanoelectromechanical systems. Understanding the thresholds of this instability helps prevent failure in graphene-based nanoelectromechanical systems, such as sensors and actuators, maintaining device performance and lifespan. In this paper, based on stress-driven nonlocal elasticity, a new size-dependent multi-beam shear model was presented to investigate the pull-in instability of multilayer graphene/substrate nano-sensors. The sensor bends towards the graphene layer because of the thermomechanical mismatch during the fabrication process. Therefore, the curvature effect is included in the proposed model. Also, the impact of the Casimir force is considered in the modeling. A finite element method has been used to simulate the nano-sensor and to obtain the pull-in instability. For validation, the pull-in voltage values obtained from the presented methodology have been compared with the results of others. Finally, considering different numbers of graphene layers and geometrical parameters such as length, initial gap, and curvature, it can be seen how these parameters affect the instability voltage of this nano-sensor. [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]

The current work investigates the transverse vibration of a piezothermoelastic (PTE) nanobeam in the frame of dual-phase-lag thermoelasticity theory. Closed-form analytical expression for the thermoelastic damping (TED) in terms of quality factor for a homogeneous transversely isotropic PTE beam is derived by using Euler–Bernoulli beam theory and complex frequency approach. The size effect of the nanostructured beam is tackled by applying modified couple stress theory (MCST). Detailed analysis on damping of vibration owing to thermal fluctuations and electric potential in the present context under three sets of boundary conditions is attempted to investigate the influences of two-phase-lag parameters, piezoelectric parameter, thermal effect and size-dependent behaviour on energy dissipation caused by TED in PTE beam resonators. Analytical results are illustrated with the help of graphical plots on numerical findings for lead zirconate titanate (PZT-5A) PTE material. The investigation brings out some significant key findings and observations in view of the present heat conduction model. [ABSTRACT FROM AUTHOR]

• An effective method is proposed to analyse the longitudinal mechanical response of shield tunnel during its construction. • The influence of the shearing dislocation of circumferential joints on the uplift of shield tunnel is fully considered. • A coefficient is introduced to accurately calculate the dynamic buoyancy generated by the synchronous grouting. • The effect of the equivalent shear stiffness of shield tunnel on the lining uplift is quantitatively analysed. During shield tunnelling, longitudinal deformation occurs in the shield tunnel structure owing to the buoyancy generated by the synchronous slurry, which has adverse effects on the assembly quality and even the structural integrity of the segmental ring structure. However, the current longitudinal beam-like model for analysing the uplift response during shield tunnel construction adopts the Euler–Bernoulli beam to describe the shield tunnel. This model does not consider the shearing dislocation effect, causing errors in the structural longitudinal deformation analysis. In this context, this study proposes a shield tunnelling uplift model based on the Timoshenko beam theory, which can effectively consider the shearing dislocation effect, aiming to evaluate the longitudinal response of shield tunnels more accurately. A Pasternak two-parameter foundation with springs reflecting the resistance of the overburden with different thicknesses was adopted to simulate the supporting effects of the synchronous grouting layer and surrounding soil layer composite on the tunnel, considering the influences of both the shearing effect of the foundation and tunnel buried depth on the shield tunnel uplift. The dynamic buoyancy coefficient, determined through an inverse analysis of the field measurement data, was introduced to accurately calculate the magnitude of the dynamic buoyancy generated by the flow of synchronous slurry. The proposed model was validated by comparing its results with actual measurements. The uplift characteristics of the shield tunnel during construction were obtained by using the proposed model in an actual project. It was found that the longitudinal analysis model for shield tunnel uplift based on the Euler–Bernoulli beam theory underestimates the uplift and overestimates the internal forces generated during shield tunnelling. [ABSTRACT FROM AUTHOR]

A novel metamaterial periodic multi-span beam with elastic supports and local resonators is designed and studied. The vibration characteristics of the designed metamaterial multi-span beam structure are investigated by the spectral element method (SEM) combined with the transfer matrix method (TMM). The accuracy and feasibility of the theoretical methods are validated by the finite element method (FEM) and vibration experiment. It is demonstrated that the metamaterial periodic multi-span beam with elastic supports can produce local resonance bandgaps in the low-frequency regions and Bragg bandgaps in the middle- and high-frequency regions. For some support stiffnesses, the amplitudes and widths of the bandgaps for the proposed structure are larger than those of the metamaterial multi-span beam with simply supported boundaries. Thus, the positions and ranges of the Bragg bandgaps can be adjusted by changing the stiffness of the elastic supports so as to improve the vibration reduction performance of the structure. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic response of an infinite Euler beam that was mounted on a fractional-order Pasternak viscoelastic foundation subjected to a moving point load was investigated. An analytical solution to the problem was derived using Fourier and Laplace transforms. Numerical results obtained by numerical Laplace inversion were analyzed to explore the impact of various parameters on the system's response. The findings indicated that increasing system damping led to a decrease in maximum deflection and a more visible deformation hysteresis with an increase in fractional derivative orders. Additionally, all parameters of the foundation and shear layer were observed to have a significant effect on the deflection. The study confirmed that the fractional-order model predicted damping and dynamic deflection more accurately than the conventional integer-order foundation model. The research contributed to the understanding of the behavior of Euler beams mounted on viscoelastic foundations and provided valuable insights into the design of such systems. [ABSTRACT FROM AUTHOR]

The optimal position and minimum support stiffness of a vibrating Timoshenko beam are investigated to maximize the fundamental frequency. The finite element method is employed. According to the maximum-minimum theorem of Courant, the optimum position is at the zero of the second mode shape function. The intermediate support's position and minimal stiffness for a wide variety of slenderness proportions were achieved. It was observed that the ideal position of intermediate support and its minimum stiffness are sensitive to the slenderness ratio. Also, for thick cantilever beams with intermediate support at the optimal location, the minimum support stiffness is less than 266.9, which was reported in the literature for the Euler-Bernoulli beam. The minimum stiffness of familiar end conditions of an optimally located beam is presented for a wide range of slenderness ratios. Since, in many practical applications, it is impossible to locate support at the optimal position, the minimum support stiffness for a beam in which its intermediate support is not located at the optimal position is obtained for various boundary conditions and slenderness ratios. Furthermore, empirical evaluations were carried out, and the findings were contrasted with hypothetical estimates of the initial two natural frequencies. [ABSTRACT FROM AUTHOR]

It is inevitable that carbon nanotubes (CNTs) are subjected to random vibrations due to environmental noise, which may impair their mechanical properties. The nonlinear dynamics associated with single-walled carbon nanotubes (SWCNTs) under random noise has been investigated in this work. First, based on the nonlocal theory and the Euler–Bernoulli beam model with fixed supports at both ends, the governed equations and boundary conditions are established according to Hamilton’s principle. Second, the Galerkin method is used to approximate the differential equations of motion and the stochastic averaging method (SAM) is applied to predict the approximate response of the original system. Subsequently, a detailed parametric study is conducted to analyze the nonlinear random vibration response of the SWCNT with nonlocal effects, and the effectiveness of the proposed method is verified by comparing the analytical results with those from the Runge–Kutta method. Finally, by solving the backward Kolmogorov (BK) equation and the generalized Pontryagin (GP) equation simultaneously, the conditional reliability function (CRF) and mean first-passage time (MFPT) for determining the reliability of SWCNT systems are obtained. [ABSTRACT FROM AUTHOR]

Theoretical studies on the vibration of microcantilever beams in fluids, which are commonly used in micro- and nanoelectromechanical systems (MEMS/NEMS). When microcantilever beams are subjected to photo-thermal excitation, they show that the material properties such as the dynamic response and the one-dimensional temperature field will show significant differences from the macroscopic properties when the size appearance of the microbeam decreases to the scale below a dozen micrometers. In this paper, by correcting the scale constants of the beams, the photothermal vibration model of the microbeam is established using the physical neutral plane theory. The one-dimensional heat transfer equations and scale-corrected temperature field of the microcantilever beam under laser excitation are derived, which are solved by Galerkin’s method, based on the theory of thermoelasticity, the hydrodynamic model of the beams vibrating in incompressible liquids proposed by Sader et al. and the theory of Euler–Bernoulli beams. The equations governing the vibration of micro-cantilever beams corrected for scale effects in different fluids when subjected to photothermal excitation are obtained. The results show that the temperature field, resonant frequency, and quality factor of the microbeam will have a significant upward drift when the size of the microbeam is close to the scale parameter, and the scale effect has a non-negligible influence on the macroscopic performance parameters; the upward drift is gradually weakening when the thickness to scale ratio gradually increases. Finally, the property of the beam is almost the same as that of the theory when the thickness of the beam is 10 times the scale constant. The correction of the theory by the scale effect is insignificant. [ABSTRACT FROM AUTHOR]

We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable to nonlocal solid mechanics, especially nonlinear elasticity. This nonlocal gradient was introduced in an earlier work, inspired by Riesz' fractional gradient, but suitable for bounded domains. The main assumption on the integrand of the energy is polyconvexity. Thus, we adapt the corresponding results of the classical case to this nonlocal context, notably, Piola's identity, the integration by parts of the determinant and the weak continuity of the determinant. The proof exploits the fact that every nonlocal gradient is a classical gradient. [ABSTRACT FROM AUTHOR]

In this study, thermomechanical behavior of regular porous materials is studied using analytical, numerical, and experimental approaches. Analytical relationships for octahedral lattice structure have been obtained based on Euler-Bernoulli beam theory. Three types of finite element models, two based on beam elements and one based on volumetric elements, are made. Additive manufacturing technique is also used to fabricate lattice structures with different relative densities. The manufactured samples are heated to a certain temperature in a closed chamber, and the displacements are measured and compared to their analytical and numerical counterparts. Based on the results, the analytical, numerical, and experimental results are in excellent agreement with each other. The methodologies introduced in this study would be beneficial for further studies on porous materials and lattice structure with other topologies and higher degrees of freedom. [ABSTRACT FROM AUTHOR]

In light of the certainty of size effect on heat conduction process in extremely small dimensions, the present article seeks to introduce a new theoretical framework for thermoelastic damping (TED) in micro-/nanobeam resonators with circular cross section by utilizing the non-Fourier model of nonlocal dual-phase-lag (NDPL). The first stage involves using NDPL model in order to develop the non-Fourier heat equation of circular cross-sectional beams in polar coordinates. This differential equation can be solved to arrive at temperature distribution in any arbitrary point of the beam. When the constitutive equations of the beam together with the extracted temperature distribution are substituted in the energy-based formulation of TED, an infinite series is produced as the TED relation in the context of NDPL model. Through a comparison study, the reliability of the acquired formula is analyzed. To shed light on how some key factors like nonclassical parameters of NDPL model, beam dimensions and material affect TED, several numerical data are prepared. As per the acquired outcomes, notably at high frequencies of oscillation, the use of NDPL model may profoundly impact the quantity and pattern of TED. [ABSTRACT FROM AUTHOR]

In this paper, an effective numerical Bernstein polynomials operational matrix is exploited to study the nonlinear forced vibration of fractional viscoelastic curved beam with viscoelastic nonlinear boundary conditions, for the first time. The Caputo fractional derivative is employed to incorporate viscoelastic material having nonlinear behavior. Based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity, the governing equation of viscoelastic curved beam which is a nonlinear integro-partial fractional differential equation is introduced. Based on the collocation method of Bernstein polynomials approximation, the generalized integer-order operational matrices of differentiation and integration as well as fractional-order operational matrix of differentiation are derived. Using Bernstein polynomials operational matrices (BPOM), the nonlinear static problem is discretized; then, it is solved via Newton's method. To compute the linear vibration mode, the linear vibration problem is discretized via BPOM and it is solved as a linear eigenvalue problem. Discretized by the Galerkin approximation, the fractional-order nonlinear integro-partial differential equation is transformed into a nonlinear fractional-order duffing-type equation. The fractional-order duffing equation is discretized using BPOM resulting nonlinear eigenvalue problem, which can be easily solved by pseudo-arc length continuation algorithm. The effects of the Caputo fractional derivative order, foundation parameters, amplitude of initial curvature, viscoelastic parameters and amplitude of excitation force on the nonlinear forced vibration of the viscoelastic beam are investigated through a detailed parametric study. The proposed procedure is supportive in the analysis and design of curved viscoelastic structure with non-classical viscoelastic boundary conditions under the dynamic mechanical loads. [ABSTRACT FROM AUTHOR]

Environmental vibration energy harvesting has received widespread attention recently, but existing research mainly focuses on cantilever beams. The fixing method of the cantilever beams limits its application range. A theoretical model and experimental results of a rectangular piezoelectric beam's modal frequencies and environmental vibration energy harvesting capacity are presented in this study. Accurate evaluation of piezoelectric beams' modal frequencies and energy harvesting capacity is extremely important to monitor and harvest energy from environmental vibrations. This paper establishes a model for the modal frequencies and response of a rectangular piezoelectric beam based on the Euler-Bernoulli beam theory and piezoelectric constitutive equation. In this paper, a fixed-size rectangular piezoelectric beam was selected for verification. The theoretical model was calculated using the modal superposition method. Then, the modal frequencies of piezoelectric beams were simulated using COMSOL, which is a multiphysics simulation software, and compared with theoretical values. Next, the modal frequencies of the piezoelectric beams and the vibration response of the theoretical results were verified through multiple sets of experiments. The experimental results show that the theoretical evaluation error of the modal frequencies of the piezoelectric beams is 1.23%, and the calculation average errors of the output voltage and power of the rectangular piezoelectric beams are 2.7% and 12.3%. The theoretical model effectively predicted the modal frequencies, output voltage, and power of the rectangular piezoelectric beams, demonstrating its potential for monitoring and harvesting environmental vibration energy. [ABSTRACT FROM AUTHOR]

A new generation of advanced composite materials has recently emerged through the use of Carbon Nanotubes (CNTs) as the reinforcing constituent in polymer matrix. In this paper, the dynamic response of polymer sandwich beams with functionally graded face sheets subject to two successive harmonic moving loads has been studied. Three different patterns of CNT's distributions for the face sheets have been investigated: Uniform Distribution (UD), Symmetrically Functionally Graded (SFG) distribution, and Unsymmetrically Functionally Graded (USFG) distribution. A thorough study on the effects of velocity, position, excitation frequency, and the phase angles of loads has been carried out using the Radial Point Interpolation Meshfree (RPIM) method based on the 2D theory of elasticity. The SFG is found to result in the highest stiffness of all three distribution patterns. Increasing the volume fraction of the reinforcement is seen to have resulted in an increase of around 33% in the flexural rigidity of the SFG beam. Also, decreasing the frequency is seen to have suppressed the deflection of the USFG type up to 90%. The current research presents a reliable computational framework to help provide an insight into the design of an optimum sandwich structure subject to a complicated state of loading. [ABSTRACT FROM AUTHOR]

The vibrations in functionally graded porous Cu-Si microcantilever beams are investigated based on physical neutral plane theory, modified coupled stress theory, and scale distribution theory (MCST&SDT). Porous microcantilever beams define four pore distributions. Considering the physical neutral plane theory, the material properties of the beams are computed through four different power-law distributions. The material properties of microcantilever beams are corrected by scale effects based on modified coupled stress theory. Considering the fluid driving force, the amplitude-frequency response spectra and resonant frequencies of the porous microcantilever beam in three different fluids are obtained based on the Euler–Bernoulli beam theory. The quality factors of porous microcantilever beams in three different fluids are derived by estimating the equation. The computational analysis shows that the presence of pores in microcantilever beams leads to a decrease in Young's modulus. Different pore distributions affect the material properties to different degrees. The gain effect of the scale effect is weakened, but the one-dimensional temperature field and amplitude-frequency response spectra show an increasing trend. The quality factor is decreased by porosity, and the degree of influence of porosity increases as the beam thickness increases. The gradient factor n has a greater effect on the resonant frequency. The effect of porosity on the resonant frequency is negatively correlated when the gradient factor is small ( n < 1 ) but positively correlated when the gradient factor is large ( n > 1 ). [ABSTRACT FROM AUTHOR]

This work aims at studying the interfacial behavior of functionally graded coatings (FGCs) on different substrates, here modeled as asymmetric double cantilever beams, in line with the experimental tests. An enhanced beam theory (EBT) is proposed to treat the mixed-mode phenomena in such specimens, whose interface is considered as an assembly of two components of the coating/substrate system bonded together partially by an elastic interface. This last one is modeled as a continuous distribution of elastic–brittle springs acting along the tangential and/or normal direction depending on the interfacial mixed-mode condition. Starting with the Timoshenko beam theory, we determine the differential equations of the problem directly expressed in terms of the unknown interfacial stresses, both in the normal and tangential directions. Different distribution laws are implemented to define the functional graduation of the material in the thickness direction of the specimens, whose variation is demonstrated numerically to affect both the local and global response in terms of interfacial stresses, internal actions, energy quantities and load–displacement curves. The good accuracy of the proposed method is verified against predictions by a classical single beam theory (SBT), with interesting results that could serve as reference solutions for more expensive experimental investigations on the topic. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to address the issue of vibration control for a class of Euler–Bernoulli beam systems that are subject to external disturbances and input saturation. The proposed controller differs from other backstepping methods in that it employs a radial basis function (RBF) neural network to accurately estimate boundary disturbances and incorporates the hyperbolic tangent function to ensure input constraints. The nonlinear partial differential equation (PDE) model is initially derived based on Hamilton's principle to capture the dominant dynamic characteristics of the flexible beam. In the framework of the Lyapunov direct approach, an adaptive RBF neural network-based law is subsequently designed to estimate the state-related boundary disturbances. The backstepping approach is then developed to propose sufficient conditions for ensuring the stability and convergence of closed-loop systems subject to input saturation. Finally, the effectiveness and superiority of the proposed methodology are further demonstrated by comparing the simulation results of constrained backstepping controllers. [Display omitted] • The paper addresses the issue of vibration control for Euler–Bernoulli beam models. • This system is susceptible to unknown external disturbances and input saturation. • A constrained boundary controller is developed based on backstepping technology. • An RBF neural network observer is proposed to estimate the boundary disturbances. • The closed-loop stability is established by considering the above constraints. [ABSTRACT FROM AUTHOR]

This paper presents a comparison between three numerical models developed for the structural analysis of composite precast concrete sandwich panels under lateral loading. The first model is based on a full finite element analysis where “slip” between the layers is obtained from the elastic deformability of the various components. The second model is based on a simplified finite element analysis where the effect of the shear connectors is smeared and modeled through an effective shear stiffness of the insulation layer. The third approach provides closed-form expressions for evaluating the deflection and is based on the classical sandwich beam theory where the shear connectors are considered through the effective stiffness of the insulation, similar to the second model. The structural response obtained from the three models was compared for various panel configurations and good correlation was obtained. A reasonable agreement with test results from the literature was also demonstrated. Therefore, both the simplified finite element model and the classical sandwich beam theory (closed-form solution) are recommended for the elastic structural analysis and for estimating the degree of composite action at the serviceability limit state of precast concrete sandwich panels. [ABSTRACT FROM AUTHOR]

The excellent properties of graphene reinforced composites (GRC) enable them to be promising material candidates for developing high-performance and multifunctional devices and structures. When subjected to thermal environment, temperature can significantly affect the structural behaviors of these components. It is necessary to consider the effects of temperature while conducting structural analysis. This work first attempts to investigate the nonlinear vibration of functionally graded (FG) graphene nanoplatelet (GNP) reinforced composite (FG-GNPRC) dielectric beams with comprehensively considering the effects of FG distribution of the reinforcements, temperature, electrical field and damping. The established governing equations for the FG-GNPRC dielectric beam are discretized and solved by differential quadrature (DQ) and direct iterative methods. The numerical results demonstrate that the application of pre-strain can attenuate the effect of electric fields and temperature on the frequency ratio, resulting in a more stable structure. Among the FG distribution patterns as involved, the FG-GNPRC beam with profile X exhibits lower frequency ratio and higher stability. This work is envisaged to provide guidelines for the design of FG-GNPRC structures with optimized performances in thermal environment. [ABSTRACT FROM AUTHOR]

Principal-internal joint resonance of an axially moving beam with elastic constraints is investigated, where the beam is located in magnetic field excited by current-carrying wires. Based on the magnetoelasticity theory and Hamilton principle, the nonlinear magneto-elastic vibration equations are derived. The displacement function is obtained by the elastic constraint boundary condition, and then the equation is discretized into 2-DOF ordinary differential equations using the Galerkin integral method. The method of multiple scales is employed for obtaining the amplitude–frequency response equations with coupling of the first two vibration modes. Through examples, amplitudes varying with frequency tuning parameter, axial velocity, current intensity, and external excitation force are exhibited. Results indicate that as current intensity increases, electromagnetic damping increases and the amplitude decreases; As external excitation force increases and axial velocity decreases respectively, the amplitude increases and the system changes from single periodic motion to quasi-periodic motion and then to single periodic motion; The lower-order modes are always dominant when the principle-internal resonance occurs. [ABSTRACT FROM AUTHOR]

In this study, we investigated the effect of hygrothermal loads on the nonlinear free vibrations of a porous bi-directional functionally graded Timoshenko beam with a Winkler–Pasternak foundation. The corresponding governing equations were established according to Hamilton's principle and von Kármán nonlinearity assumption. Using the differential quadrature and iterative methods, the nonlinear fundamental frequencies were determined. A numerical example was presented, and we showed that the discretization of nonlinear items considerably decreased the number of iterations. A series of parametric studies were performed, and we determined that (1) all the vibration mode shapes were significantly affected by the axial functionally graded index, while they were almost unchanged by the thickness-wise functionally graded index. Moreover, compared to the thickness-wise graded index, the axial functionally graded index played a more important role in the higher-order mode shapes. (2) The geometric nonlinearity considerably influenced the critical temperature rise value of the beams. Increasing the maximum deflection value increased the critical temperature rise value. (3) The influence of increase in temperature and moisture on the nonlinear fundamental frequency became stronger with increase in the functionally graded index, but it weakened with increase in the maximum deflection value. [ABSTRACT FROM AUTHOR]

AbstractThis study presents the buckling and lateral torsional buckling behaviors of thin-walled laminated composite or functionally graded sandwich I-beams. A refined beam model (RBT) based on the 3D Saint-Venant (SV) solution is used in this study to formulate the problem. This model allows for a realistic analysis of beams with arbitrary cross-sections and is free from the limitations of classical beam theories. The displacement models establish a consistent 1D beam theory that accurately captures the essence of the cross-section’s nature. The governing models consider cross-section deformations, including in and out of plane warpings and distortions derived from the 3D SV solution associated with the cross-section vibrational behavior. Furthermore, a user-friendly numerical tool called CSB (cross-section and beam analysis) is used to facilitate the implementation of this method. The numerical results are examined in detail and compared with previous works to investigate the influence of boundary conditions, angle-ply, shear effects, span-to-height ratio, and material distribution on the critical buckling loads of thin-walled I-beams. The results demonstrate that the RBT models accurately and efficiently analyze thin-walled I-beams under different loads and boundary conditions. Furthermore, some of the new results are presented as reference values for the future. [ABSTRACT FROM AUTHOR]

In this paper, we present a study of vibration characteristics of the double-beam structures combined with the concept of the acoustic black hole (ABH), which is an effective technique for vibration and noise control. In the proposed double-beam structure, the ABH beam as the vibration damper is attached to the primary uniform beam by a range of translational and rotational springs. We formulate the closed-form spectral element matrix of the double-beam structure and calculate the natural frequencies and mode shapes of the system. The results demonstrate the ABH effect of increasing the modal damping ratios. We also study the power flow and mechanical intensity of the system to offer physical insight into the vibration suppression mechanism of the ABH. A detailed parametric analysis of both translational and rotational springs is carried out. The investigation contributes to the exact dynamic modelling and analysis of the double-beam system containing ABH elements. Furthermore, the proposed ABH double-beam structure shows great potential for vibration control and energy harvesting. [ABSTRACT FROM AUTHOR]