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This paper investigates the nonlinear free vibration of spinning pre-twisted functionally graded material (FGM) plates in thermal environment. Based on the Kirchhoff plate theory and von Kármán large-deformation theory, the nonlinear dynamic model is established via the Lagrange equation, where the warping effect is taken into account. The material properties are related to temperature and change according to a power-law exponent distribution. The theoretical solution of nonlinear-free vibration is obtained using the multiple scale method. The effects of power-law exponent, temperature difference, spinning speed, hub radius ratio, and twist angle on nonlinear-free vibration characteristics of the spinning pre-twisted cantilever FGM plates are discussed. The results show that the spinning pre-twisted cantilever FGM plate exhibits nonlinear hardening-spring vibration behavior, while the characteristics weaken with the increase of spinning speed. The twist angle and setting angle have coupling effects on the nonlinear vibration characteristics of spinning pre-twisted FGM plates. [ABSTRACT FROM AUTHOR]

In this article, theoretical modeling and vibration characteristics of a spinning double-blade beam assembly restricted by elastic supports are studied. Graphene nanoplatelet (GPL) reinforcement and porous foamed metal matrix are adopted to make up the assembly structure. Due to the nonuniformity of the porosity and graphene nanofillers, the material properties of the attached blades and beam are considered to change along the blade thickness and beam radius, respectively. They are obtained via the rule of mixture, the open-cell scheme and the Halpin-Tsai micromechanics model. These attached blades and beam are modeled in accordance with the Euler-Bernoulli beam theory and the Rayleigh beam theory, respectively. Via employing the Lagrange's equation, the equations of motion of the double-blade beam are derived. Then, the natural frequencies of the spinning nanocomposite double-blade beam are calculated by the substructure modal synthesis method and the assumed modes method. A detailed parameter analysis is performed to study the influences of dimension, distribution pattern and weight fraction of GPLs, distribution and coefficient of porosity, length and location of the blades, stiffness and location of supports, and spinning speed on the mechanical behaviors of the double-blade beam assembly. [ABSTRACT FROM AUTHOR]

This paper presents an investigation on vibration characteristics of graphene nanoplatelet (GPL) reinforced disk-shaft rotor with eccentric mass resting on elastic supports. The shaft is made of common metal material while the disk is made of graphene nanoplatelet reinforced material. The weight fraction of graphene nanoplatelets (GPLs) is assumed to vary smoothly and continuously along the thickness direction of the disk, which leads to a functionally gradient (FG) structure. The effective properties of the disk are determined via the Halpin-Tsai micromechanics model and the rule of mixture. In accordance with the Timoshenko beam theory and Kirchhoff plate theory, the governing equations which take into account gyroscopic effect due to rotation are derived by using the Lagrange equation. The substructure modal synthesis method and the assumed modes method are utilized to obtain the natural frequencies, and the Runge-Kutta method is adopted to solve the forced vibration response of the rotor system, where the centrifugal force and gravity of an eccentric mass in the shaft are considered as generalized forces. The present analysis is validated through comparison with both experiment and finite element (FE) results. A detailed parametric study is conducted to examine the effects of the rotating speed, GPL weight fraction, GPL distribution pattern, length-to-thickness ratio and length-to-width ratio of GPLs, disk position, disk dimension, and support stiffness on vibration behaviors of the nanocomposite disk-shaft rotor system. [ABSTRACT FROM AUTHOR]

For three-dimensional (3-D) vibration suppression of flexible beams, the most commonly used method is the boundary-controlled strategy, which is challenging to employ in general environments. In this study, a novel strategy by employing planned-motion flywheel assembly is designed to suppress 3-D vibration of flexible beams, which is easier to implement and more widely applicable than the boundary-controlled strategy. First, the dynamic equations of flexible beams with flywheel assembly are derived based on the Lagrange equation, where the Euler-Bernoulli beam theory and the geometric nonlinearity are employed. Subsequently, the phase delay method is employed to plan the motion of the flywheel assembly, while the optimal parameters in the expressions of flywheel assembly's motion are derived through the analysis of system energy. Theoretical results suggest that the flywheel assembly with planned motion enables the beam stable rapidly in free vibration and decreases displacement in forced vibration. Experimental results also demonstrate this strategy can enable the beam stable rapidly in free vibration under various initial conditions. The proposed control strategy can provide effective 3-D vibration suppression in flexible beams. [ABSTRACT FROM AUTHOR]

Bolt connection is commonly used to assemble shell structures in engineering fields. Prolonged external excitation can induce stick, slip, even separation states at the connection interface, leading to complex nonlinear dynamics in bolted shell structures. Understanding the dynamic mechanism of bolted joined shells under stick–slip-separation condition is crucial for the design and application of these structures. In this study, we aim to build the nonlinear dynamic model and reveal the vibration mechanism of bolted joined conical-cylindrical shells with stick–slip-separation behavior. During the development of the mechanical model of the bolt connection, the axial bilinear stiffness characteristics and interface friction behaviors are taken into account simultaneously, which could simulate the transition of the contact state at the connection interface. The rigid joint between the conical and cylindrical shells is realized via successive distributed artificial springs. Donnell's shell theory as well as the displacement assumption of Chebyshev polynomials are employed in theoretical modeling, and the governing equation is obtained by the Lagrange equation. In contrast with existing research and experimental data, the accuracy of the present theoretical model is validated. Both theoretical and experimental results indicate the frequency multiplication and dynamic softening phenomena as the excitation level increases. By the consideration of the stick-slip-separation behavior at the connection interface in the modeling, these nonlinear vibration behaviors can be effectively illustrated. Additionally, hysteresis characteristics are further investigated to explore frictional energy dissipation. The stick–slip-separation contact state at the connection interface under different excitation levels, bolt preloads and cone angles are also analyzed. The present investigation provides a basis for the design and health condition monitoring of bolted shell structures. [ABSTRACT FROM AUTHOR]

The theoretical modeling of a functionally graded (FG) graphene nanoplatelet (GPL)-reinforced assembled beam–plate structure resting on elastic supports is presented for the first time, and its free vibration analysis is performed. Herein, the assembled structure is modeled according to the Kirchhoff plate theory and the Rayleigh beam theory. The graphene nanoplatelets (GPLs) gradiently distribute in the beam's radial direction and in the plate's thickness direction, respectively. By adopting the rule of mixture and the Halpin–Tsai model, the effective material properties can be obtained. By employing the Lagrange's equation and considering the effects of Coriolis force and centrifugal force, the coupled governing equations of the assembled structure are determined. Furthermore, the assumed modes method and substructure modal synthesis method are applied to obtain the frequencies of the assembled beam–plate structure. A comprehensive numerical investigation is carried out to discuss the influence of the structural and material parameters on the vibration behavior of the beam–plate structure. [ABSTRACT FROM AUTHOR]

• Dynamic model of shaft-disk rotors in axial non-uniform temperature field is developed. • Three-dimensional displacement fields for both shaft and disk are considered. • Temperature-dependent material properties are considered. • Present model can effectively predict vibrations of shaft-disk rotors in axial non-uniform temperature field. • Effect of non-uniform temperature field is related to the rotational speed and disk location. Research on vibrations of shaft-disk rotors in non-uniform thermal field is essential for the design of rotating machinery. In this paper, the dynamic model of axially loaded thin-walled shaft-disk rotors in axial non-uniform temperature field is developed, considering three-dimensional displacement fields of the shaft and disk. This model introduces the temperature-dependent properties of materials, and gyroscopic and centrifugal effects. Based on the Euler-Bernoulli beam theory and the Kirchhoff plate theory, Lagrange's equation is used to derive the differential equations of motion. By comparing with the results of the existing reference and finite element results, the accuracy of the present model is verified. The effects of the axial displacement of shaft, temperature-dependent material property, temperature difference, temperature distribution, disk position and axial preload on the free vibration of shaft-disk rotors are discussed. Results show that the present model can effectively predict free vibrations of shaft-disk rotors in axial non-uniform temperature field. The effect of thermal field on vibrations of shaft-disk rotors is affected by the rotational speed and disk location as well. [ABSTRACT FROM AUTHOR]

• Nonlinear dynamics of bolted JCCSs are studied theoretically and experimentally. • Displacement-dependent characteristics in bolt connection zone are considered. • The developed model is capable of predicting nonlinear vibration of bolted JCCSs. • Experimental results validate the present theoretical model. This paper investigates the nonlinear dynamic characteristics of joined conical-cylindrical shells (JCCSs) with bolt connection for the first time. In the process of developing mechanical model of the bolt connection, the displacement-dependent stiffness and damping are taken into account, which could simulate the change of the contact state at the connection interface under different excitations. Both theoretical and experimental studies are performed to illustrate the nonlinear vibration behaviors of the bolted JCCSs. Successive uniform distributed artificial springs between the conical and cylindrical shells are adopted to simulate the rigid joint of the two shells. Donnell's shell theory is employed in theoretical modeling, and the governing equation is obtained by the Lagrange equation. The displacement admissible function applied in the research is Chebyshev polynomial. By comparison with existing literature and experimental data, the accuracy of present theoretical model is validated. It is found that both theory and experiment show a dynamic softening phenomenon with the increase of excitation level. Taking the displacement-dependent characteristics in bolt connection zone into consideration can effectively illustrate this soft phenomenon. The established model is capable of predicting the nonlinear vibration characteristics of JCCSs with bolt connection. [Display omitted] [ABSTRACT FROM AUTHOR]

• Vibrations of JCCSs with bolt loosening boundary are studied theoretically and experimentally. • Non-uniform arc constraint is established to simulate the bolt loosening boundary. • The developed model is reliable in estimating the dynamic behaviors of bolted JCCSs with different loosening degrees. • Experimental results validate the present theoretical model. This paper investigated the vibration characteristics of joined conical-cylindrical shells (JCCSs) with bolt loosening boundary conditions both theoretically and experimentally. The non-uniform arc constraint model is established to simulate the bolt loosening boundary conditions by the artificial spring technology, which can describe the actual bolt contact pressure distribution. Continuously distributed artificial springs are introduced to realize the connection of the conical and cylindrical shells. Donnell's shell theory and Chebyshev polynomials are adopted to establish the theoretical model, and the dynamic equation is derived from the Lagrange equation. The validity of the present model is verified by the available literature, hammer test and vibration shaker test. The results indicate that the maximum errors of natural frequencies and resonant displacements are less than 4.41% and 18.6%, respectively. It is found that bolt loosening has a significant effect on the fundamental frequency, but it gradually weakens with the increase of the mode order. Increasing bolt loosening degree can lead to an increment of resonant displacement. The developed model is reliable in estimating the dynamic behaviors of bolted JCCSs with different loosening degrees, and it contributes to providing guidance in the design and service process of combined shell structures. [ABSTRACT FROM AUTHOR]

This paper develops a semi-analytical method for solving the frequency response of spinning cylindrical shells. The dynamic model of the spinning cylindrical shells with discontinuous boundary conditions is established. In the modeling, Sanders' shell theory is employed and Chebyshev polynomials are adopted as the admissible displacement functions. By using the Lagrange equation, the equation of motion is obtained. Then, the equation is transformed into a state-space form, wherein the orthogonality of complex eigenvectors is derived. Further, the equation of motion is decoupled on the basis of the complex mode theory. Utilizing the reduced complex eigenvector, a semi-analytical method for solving the frequency response of the spinning shells is finally developed, wherein the point and distributed harmonic loads are all considered. The influences of the damping coefficient, the spinning speed, and the boundary spring stiffness on the frequency response of the shells are analyzed. The proposed method can conveniently predict the vibration characteristics of spinning cylindrical shells through a reduced-order dynamic model, which is much more efficient than numerical methods. • A semi-analytical method for solving the frequency response of spinning cylindrical shells is developed. • Discontinuous boundary conditions are introduced by artificial springs technology. • Complex mode theory is applied to decouple the equation of motion. • Frequency-response explicit functions for both point and distributed harmonic loads are obtained. [ABSTRACT FROM AUTHOR]

Internal resonances in circular cylindrical shells, induced by the spinning motion, are explored in this research. The mathematical model of spinning cylindrical shells is established by employing Donnell's nonlinear shell theory and the Lagrange equations of motion. Then, the nonlinear forced vibration responses of the shells are solved by using the pseudo-arclength continuation technique. Some comparisons are conducted to verify the accuracy of the present model and method The results show that internal resonances can be caused by the spinning motion of the shells, which cover a wide range of spinning speeds. Different types of internal resonances can occur, such as 1:1, 1:1:1, and 1:2 internal resonances. Energy exchanges between different modes with internal resonance relationships. Both softening and hardening nonlinearities exist in the frequency response of the spinning cylindrical shells. The excitation amplitude has a threshold to excite the internal resonances. It is found that the internal resonances can be avoided by tuning the spinning speed of the shells. • Internal resonances can be induced by the spinning motion of circular cylindrical shells. • Internal resonances in circular cylindrical shells cover a wide range of spinning speeds. • Different types of internal resonances are discovered in spinning circular cylindrical shells. • Internal resonances can be avoided by tuning the spinning speed of the shells. [ABSTRACT FROM AUTHOR]

• The piezo-actuated beam model considering the neutral surface offset caused by the piezoelectric actuator is established and the LADRC algorithm is designed. • Modal experiment and AVC experiment of the piezo-actuated beam are carried out. • The AVC of the piezo-actuated beam is studied by using theoretical and experimental methods. • The vibration suppression performance of the LADRC algorithm on piezo-actuated beams is studied, and the adaptability and anti-noise ability of the LADRC algorithm are explored. The active vibration control (AVC) of lightweight thin-walled structures on spacecraft has been a proven solution for vibration suppression. In this study, a linear active disturbance rejection control (LADRC) algorithm is presented for vibration suppression of piezo-actuated beams. Firstly, the governing equation of a piezo-actuated beam is obtained by using the Euler–Bernoulli beam theory and the Lagrange equation. The LADRC algorithm is designed for the piezo-actuated beam based on the governing equation. Then, the accuracy of the piezo-actuated beam model is confirmed by comparison with ANSYS and experiments. Finally, numerical simulations and experiments are carried out on the active vibration suppression of the piezo-actuated beam under the fixed harmonic excitation, variable harmonic excitation, and fixed harmonic excitation with measuring noise, respectively. The results show that the LADRC algorithm has an excellent control effect on structural vibration suppression, strong adaptability to various external excitations, and anti-noise ability. [ABSTRACT FROM AUTHOR]