Three-dimensional elasticity analysis of a laminated cylindrical shell with piezoelectric layer under dynamic loads

Abstract

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.

Dynamic analysis of a laminated cylindrical shell with piezoelectric layer and clamped boundary condition

“…where η is the absolute permittivity constant of piezoelectric material. To comply with the simplysupported shell results [14], the following non-dimensionalisations have been used:…”

“…In Fig. 4a comparison between the radial displacements through the thickness of clamped and simply-supported boundary conditions [14] for sensor case is presented. For thick shell a 6.66% reduction and for thin shell a 3.1% reduction is observed in the mid layer.…”

“…Fig. 7 compares the radial stress distribution through the thickness for clamped and simply-supported boundary conditions [14], the piezo-layer serves as sensor. The boundary and inter laminar conditions of radial stress are satisfied in this figure.…”

“…A finite element formulation using the layerwise theory, developed for laminated cylindrical shell with piezoelectric layers subjected to dynamic load, besides the 3-D elasticity solution has been studied [13]. The elasticity solution for simply-supported, laminated cylindrical shell with piezoelectric layer subjected to dynamic load has been presented by the author [14]. The resulting equations are solved by Galerkin's finite element in radial direction.…”

Dynamic analysis of a laminated cylindrical shell with piezoelectric layers under dynamic loads

“…A finite element formulation using the layerwise theory, developed for laminated cylindrical shell with piezoelectric layers subjected to dynamic load, besides the 3D elasticity solution has been studied [13]. The elasticity solution for simply supported, laminated cylindrical shell with piezoelectric layer subjected to dynamic load has been presented by the authors [14]. The resulting equations are solved by Galerkin's finite element in radial direction.…”