Search

The thermo-electro-mechanical nonlinear vibration of circular cylindrical nanoshells on the Winkler–Pasternak foundation is investigated. The nanoshell is made of functionally graded piezoelectric material (FGPM), which is simulated by the nonlocal elasticity theory and Donnell's nonlinear shell theory. The Hamilton's principle is employed to derive the nonlinear governing equations and corresponding boundary conditions. Then, the Galerkin's method is used to obtain the nonlinear Duffing equation, to which an approximate analytical solution is obtained by the multiple scales method. The results reveal that the system exhibits hardening-spring behavior. External applied voltage and temperature change have significant effect on the nonlinear vibration of the FGPM nanoshells. Moreover, the effect of power-law index on the nonlinear vibration of the FGPM nanoshells depends on parameters such as the external applied voltage, temperature change and properties of the Winkler–Pasternak foundation. [ABSTRACT FROM AUTHOR]

In this paper, free vibrations of cylindrical nanoshells made of nanoporous metal foam are investigated for the first time. Based on the modified couple stress theory and Love's thin shell theory, the governing equations of the present system are derived by using Hamilton's principle. Two types of nanoporosity distribution are considered in the construction of the nanoporous shells. Then, the Navier method and Galerkin method are utilized to solve natural frequencies of the nanoporous shells under different boundary conditions. Afterwards, a detailed parametric study is conducted. Results show that the nanoporosity type, the material length scale parameter, the porosity coefficient, the length-to-radius ratio, and the radius-to-thickness ratio play important role on the free vibrations of nanoporous shells. To check the validity of the present analysis, the results are compared with those in previous studies for the special cases. [ABSTRACT FROM AUTHOR]

To provide reference for aerospace structural design, electro-mechanical vibrations of functionally graded piezoelectric material (FGPM) plates carrying porosities in the translation state are investigated. A modified power law formulation is employed to depict the material properties of the plates in the thickness direction. Three terms of inertial forces are taken into account due to the translation of plates. The geometrical nonlinearity is considered by adopting the von Kármán non-linear relations. Using the d’Alembert's principle, the nonlinear governing equation of the out-of-plane motion of the plates is derived. The equation is further discretized to a system of ordinary differential equations using the Galerkin method, which are subsequently solved via the harmonic balance method. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge-Kutta technique. Additionally, the stability of the steady state responses is examined by means of the perturbation technique. Linear and nonlinear vibration analyses are both carried out and results display some interesting dynamic phenomenon for translational porous FGPM plates. Parametric study shows that the vibration characteristics of the present inhomogeneous structure depend on several key physical parameters. [ABSTRACT FROM AUTHOR]

Vibrations of longitudinally traveling functionally graded material (FGM) plates with porosities are studied for the first time. The FGM plates contain porosities owing to the technical issues during the preparation of FGMs. Two different porosity distributions, namely, even and uneven distribution, are considered in this paper. The large-amplitude motion of FGM plates is taken into account so that the present model includes both geometry and material nonlinearities. The governing equation of the present system is derived by using the D'Alembert's principle. The Galerkin method is utilized to discretize the governing equation to a system of ordinary differential equations. The method of harmonic balance is adopted to perform an approximately analytical analysis on the present model. Then the analytical results are validated by the comparison with numerical solutions, which are obtained by using the adaptive step-size fourth-order Runge-Kutta method. Moreover, the stability of steady-state analytical solutions is analyzed. Nonlinear vibrational responses for both FGM plates with evenly distributed porosities (EDP) and unevenly distributed porosities (UEDP) are examined. A 1:1 internal resonance behavior is discovered and it is found that this behavior can be excited by very small external excitation. Furthermore, the effects of porosity volume fraction, damping and constituent volume fraction on the dynamic response of the system are highlighted. [ABSTRACT FROM AUTHOR]

This research focuses on the large-amplitude vibration of sigmoid functionally graded material (S-FGM) thin plates with porosities. Porosities in S-FGM plates can happen due to technical issues during the preparation of S-FGMs. Two types of porosity distribution, i.e., even and uneven distribution, are taken into account. The material properties of S-FGM plates with porosities change smoothly along the thickness direction based on the sigmoid distribution law, which is described by modified piecewise functions. The geometrical nonlinearity is considered by applying the von Kármán non-linear plate theory. The nonlinear governing equation of S-FGM plates with porosities is derived using the D′Alembert's principle. By applying the Galerkin method with the first three modes, the governing equation is discretized to three ordinary differential equations. Then, the method of harmonic balance is used to solve these discretized equations. Analytical results are verified numerically with the adaptive step-size fourth-order Runge-Kutta method. The stability of the steady-state response is examined by means of the perturbation technique. Furthermore, the maximum amplitudes of each mode during the vibration period are obtained and shown in the neighborhood of the fundamental mode. Study demonstrates that the S-FGM plates with porosities possess hardening spring characteristics in nonlinear frequency response. Moreover, a complex multi-solution phenomenon occurs in the present dynamic system which is rooted from the nonlinear mode interaction. Finally, investigation is made on the effects of porosity along with other key parameters on large-amplitude vibration response of porous S-FGM plates. [ABSTRACT FROM AUTHOR]

A first known study is conducted on the vibrations of functionally graded material (FGM) rectangular plates with porosities and moving in thermal environment. The FGM plates contain porosities owing to the technical issues during the preparation of FGMs. Two types of porosity distribution, namely, even and uneven distribution, are considered. The geometric nonlinearity is taken into account by using von Kármán nonlinear plate theory. The out-of-plane equation of motion of the system is derived based on the D'Alembert's principle with the consideration of the thermal effect and longitudinal speed. Then the Galerkin method is employed to discretize the partial differential equation of motion to a set of ordinary differential equations. These time-varying ordinary differential equations are solved analytically by means of the method of harmonic balance. The accuracy of approximately analytical solutions is verified by the adaptive step-size fourth-order Runge–Kutta technique. Additionally, the stability of steady-state solutions is analyzed for the analytical solutions. Vibration characteristics such as natural frequency and nonlinear frequency response are shown. The present model is a hardening-spring system based on the nonlinear frequency response results. Effects of some key parameters are investigated on the vibration of rectangular FGM plates with porosities and moving in thermal environment. [ABSTRACT FROM AUTHOR]

This study investigates nonlinear dynamic thermoelastic response of functionally graded material (FGM) plates with longitudinal velocity for the first time. The large amplitude motion of FGM plates is considered so that the present model includes both geometry and material nonlinearities. Based on the D'Alembert's principle, the out-of-plane equation of motion of the system is obtained by considering the thermal effect and the longitudinal velocity. After that, the Galerkin method is employed to discretize the partial differential equation of motion to a set of ordinary differential equations. The method of harmonic balance is used to solve analytically the time-varying set of ordinary differential equations. The approximately analytical solutions are verified by numerical solutions utilizing an adaptive step-size fourth-order Runge-Kutta technique. Furthermore, the stability of steady-state response is analyzed for the approximately analytical solutions. The linear frequency characteristics and nonlinear frequency-response characteristics are both presented for the system. The nonlinear frequency-response relationships demonstrate strong hardening-type behavior of the system. Results are shown to examine the influences of different parameters including longitudinal velocity, temperature, constituent volume distribution, in-plane pretension, damping and force amplitude on the nonlinear dynamic thermoelastic response of FGM plates with longitudinal velocity. [ABSTRACT FROM AUTHOR]

The stability and dynamics of an axially moving unidirectional plate partially immersed in a liquid and subjected to a nonlinear aerodynamic excitation are investigated. The method of singular functions is adopted to study the dynamic characteristics of the unidirectional plates with discontinuous characteristics. Nonlinearities due to large-amplitude plate motions are considered by using the classical nonlinear thin plate theory, with allowance for the effect of viscous structural damping. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the unidirectional plate. The effect of fluid on the vibrations of the plate may be equivalent to added mass of the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate-fluid interfaces. The system is discretized by Galerkin's method while a model involving two degrees of freedom, is adopted. Attention is focused on the behavior of the system in the region of dynamic instability, and several motions are found by numerical simulations. The effects of the moving speed and some other parameters on the dynamics of the system are also investigated. It is shown that chaotic motions can occur in this system in several certain regions of parameter space. [ABSTRACT FROM AUTHOR]

A cantilever thin rotating circular cylindrical shell is investigated in this paper. The precession factor of vibrating shape is obtained by an energy approach, with damping and geometric nonlinearity considered. Donnell's shallow-shell theory is used, the non-linear equations of motion are discretized by Galerkin method, in which geometric nonlinearity and precession of vibrating shape are taken into account. The non-linear mode equations are studied by using Runge-Kutta method and harmonic balance method, and the stability of analytical solutions is studied. The results show that geometric nonlinearity does not influence the precession factor of vibrating shape but causes multi-value and leap characteristics. [ABSTRACT FROM AUTHOR]

In this work, we aim to study free vibration of functionally graded piezoelectric material (FGPM) cylindrical nanoshells with nano-voids. The present model incorporates the small scale effect and thermo-electro-mechanical loading. Two types of porosity distribution, namely, even and uneven distributions, are considered. Based on Love's shell theory and the nonlocal elasticity theory, governing equations and corresponding boundary conditions are established through Hamilton's principle. Then, natural frequencies of FGPM nanoshells with nano-voids under different boundary conditions are analyzed by employing the Navier method and the Galerkin method. The present results are verified by the comparison with the published ones. Finally, an extensive parametric study is conducted to examine the effects of the external electric potential, the nonlocal parameter, the volume fraction of nano-voids, the temperature rise on the vibration of porous FGPM cylindrical nanoshells. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear static and dynamic behaviors of slightly curved cantilevered pipes conveying fluid under transverse base excitations are investigated. Incorporating geometrical and inertial nonlinearities, a new three-dimensional dynamic model is developed for the inextensible cantilevered pipe based on the Euler–Bernoulli beam theory. The resultant partial differential equations are discretized using the Galerkin method and solved utilizing the pseudo-arclength continuation technique and a time-integration method. The static equilibrium configuration, linear stability, and nonlinear response of the pipe are calculated for various cases, which allow us to investigate the effects of flow velocity, gravity coefficient, initial curvature amplitude and shape, and base-excitation amplitude and frequency. An emphasis is put on the importance of modal interactions on frequency-response and force-response relationships, evidencing the possible in-plane and out-of-plane transverse vibrations and identifying the preferred forms of pre- and post-instability behaviors. This study offers an efficient theoretical model for exploring the nonlinear forced response of slightly curved cantilevered pipes conveying fluid and provides a better insight for further investigations on the modal interaction in cantilevered pipe devices. [ABSTRACT FROM AUTHOR]