Electro-elasto-dynamic analysis of functionally graded cylindrical shell with piezoelectric rings using differential quadrature method

Based on an axisymmetric layerwise approach, the differential quadrature method (DQM) is adopted in axial direction to analyse a hollow cylindrical shell made of functionally graded material (FGM) with piezoelectric actuator rings under dynamic load. The mechanical properties are regulated by volume fraction as a proper function of the radial coordinate. The FGM shell and piezo-rings are divided into mathematical sub-layers in thickness direction, then the general layerwise theory is formulated through introducing piecewise continuous approximations across each sub-layer. This accounts for any discontinuity in derivatives of the displacement at the interface of the rings and the cylinder. The virtual work statement including structural and electrical potential energies yields the 3-D governing equations which are reduced to 2-D differential equations, which then are discretized by using DQM in both the spatial and time domains. By inserting the boundary conditions into the DQ form of the equations and incorporating the initial conditions, a system of algebraic equations is obtained that delivers the unknown degrees of freedom. Static and dynamic responses of the FG shell to electrical and mechanical loads with different exponents of material in homogeneity ‘ n ’ and boundary conditions as well as the effects of size, number and interval between actuated piezo-rings on the induced deformation in the FG shell are investigated. The accuracy and computational efficiency of the proposed approach are verified by comparing the results with those obtained using the finite element method and similar problems in the literature.