Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state

Now a days, sandwich beams and plates made of functionally graded (FG) materials are widely used in many engineering industries. Therefore, several modeling techniques and solution methods ...

Modeling and analysis of functionally graded sandwich beams: a review

An isogeometric Bézier finite element method for vibration analysis of functionally graded piezoelectric material porous plates

This work investigates the porosity-dependent nonlinear forced vibrations of functionally graded piezoelectric material (FGPM) plates by using both analytical and numerical methods. The FGPM plates contain porosities owing to the technical issues during the preparation of FGPMs. Two types of porosity distribution, namely, even and uneven distribution, are considered. A modified power law model is adopted to describe the material properties of the porous FGPM plates. Using D'Alembert's principle, the out-of-plane equation of motion is derived by taking into account the Karman nonlinear geometrical relations. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by employing the harmonic balance method. The approximate analytical results are verified by using the adaptive step-size fourth-order Runge–Kutta method. By means of the perturbation technique, the stability of approximate analytical solutions is examined. An interesting nonlinear broadband vibration phenomenon is detected in the FGPM plates with porosities. Nonlinear frequency-response characteristics of the present smart structures are investigated for various system parameters including the porosity type, the porosity volume fraction, the electric potential, the external excitation, the damping and the constituent volume fraction. It is found that these parameters have significant effects on the nonlinear vibration characteristics of porous FGPM plates.

https://iopscience.iop.org/article/10.1088/1361-665X/aa8429/pdf

Porosity-dependent nonlinear forced vibration analysis of functionally graded piezoelectric smart material plates

Analysis and numerical results for the free axisymmetric and non-axisymmetric vibrations of functionally graded annular plates elastically supported on the ring support have been presented on the basis of classical plate theory. The quasi-Green's function has been employed to solve to boundary value problem of free vibration of functionally graded annular plate with free outer edge and clamped, simply supported and free inner edges. Additional properties of the quasi-Green's function were presented and discussed for the functionally graded annular plate. The influence of volume fraction index, core radius, selected boundary conditions, position and stiffness of ring supports on natural frequencies of an annular plate has been comprehensively studied. Singularities as the core and support radii shrink to zero are calculated for different values of volume fraction index and stiffness of the support. The quasi-Green's function method allows us to obtain universal non-linear multiparametric characteristic equations functional dependent on radius of core, volume fraction index, position and stiffness of any amount of elastic supports or other discrete elements without necessity considering new boundary value problem or find scaling factors. Additionally, the continuity conditions between the supports and plate can be omitted in the obtained solutions of boundary value problem. The presented investigation has not been reported previously. The exact frequencies of vibration presented in non-dimensional form can serve as benchmark values for researchers and engineers to validate their numerical methods applied in many fields of engineering such us mechanical, aeronautical or production engineering.

Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green's function method

Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

This investigation focuses on the modal analysis of an axially functionally graded material beam under hygrothermal effect. The material constants of the beam are supposed to be graded smoothly alo...

Pankaj Sharma

Papers

Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

On modal analysis of axially functionally graded material beam under hygrothermal effect

Efficacy of Harmonic Differential Quadrature method to vibration analysis of FGPM beam

Modal analysis of shear-induced flexural vibration of FGPM beam using Generalized Differential Quadrature method

Vibration Analysis of Functionally Graded Piezoelectric Actuators