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The elasticity solution for simply-supported, laminated cylindrical shell with piezoelectric layer is presented. The shell is subjected to various dynamic loads. The direct piezoelectric effect is considered. The governing differential equations are reduced to ordinary differential equations by means of trigonometric function expansion for displacement and electric potential. The loading function is expanded as a double Fourier series in axial and circumferential coordinates. The resulting equations are solved by Galerkin's finite element in radial direction. The static results and natural frequencies are compared with similar ones in the literature. The effect of radius to thickness ratio and band load width on dynamic behaviour is studied. Time responses are presented for [0/90/Piezo] lamination.

The present study introduces a highly accurate numerical calculation of buckling loads for an elastic rectangular plate with variable thickness, elasticity modulus, and density in one direction. The plate has two opposite edges ( x = 0 and a) simply supported and other edges ( y = 0 and b) with various boundary conditions including simply supported, clamped, free, and beam (elastically supported). In-plane normal stresses on two opposite simply supported edges ( x = 0 and a) are not limited to any predefined mathematical equation. By assuming the transverse displacement to vary as sin( mπ x/ a), the governing partial differential equation of plate motion will reduce to an ordinary differential equation in terms of y with variable coefficients, for which an analytical solution is obtained in the form of power series (Frobenius method). Applying the boundary conditions on ( y = 0 and b) yields the problem of finding eigenvalues of a fourth-order characteristic determinant. By retaining sufficient terms in power series, accurate buckling loads for different boundary conditions will be calculated. Finally, the numerical examples have been presented and, in some cases, compared to the relevant numerical results.

The objective of this paper is to demonstrate layerwise theory for the analysis of thick laminated piezoelectric shell structures. A general finite element formulation using the layerwise theory is developed for a laminated cylindrical shell with piezoelectric layers, subjected to dynamic loads. The quadratic approximation of the displacement and electric potential in the thickness direction is considered. The governing equations are reduced to two-dimensional (2D) differential equations. The three-dimensional (3D) elasticity solution is also presented. The resulting equations are solved by a proper finite element method. The numerical results for static loading are compared with exact solutions of benchmark problems. Numerical examples of the dynamic problem are presented. The convergence is studied, as is the influence of the electromechanical coupling on the axisymmetric free-vibration characteristics of a thick cylinder.

In this paper a nonlinear approach to studying the vibration characteristic of laminated composite plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange type of strain-displacements relations, by incorporating higher-order terms arising from nonlinear relations of kinematics into mathematical formulations. The equations of motion are obtained through the energy method, based on Lagrange equations and by using higher-order shear deformation theories with von Karman-type nonlinearities, so that transverse shear strains vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch. Different boundary conditions are investigated. Optimal locations of piezoelectric patches are found using a genetic algorithm to maximize spatial controllability/observability and considering the effect of residual modes to reduce spillover effect. Active attenuation of vibration of laminated composite plate is achieved through an optimal control law with inequality constraint, which is related to the maximum and minimum values of allowable voltage in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the Pontryagin's minimum principle is implemented in a system with multi-inequality constraint of control inputs. The results are compared with similar ones, proving the accuracy of the model especially for the structures undergoing large deformations. The convergence is studied and nonlinear frequencies are obtained for different thickness ratios. The structural coupling between plate and piezoelectric actuators is analyzed. Some examples with new features are presented, indicating that the piezo-patches significantly improve the damping characteristics of the plate for suppressing the geometrically nonlinear transient vibrations.