This study investigates the free vibration behavior of cylindrical panels and shells of revolution integrated with piezoelectric patches. Based on the first-order shear deformation theory and Hamilton’s principle, the mechanical equations of the shell and panel are formulated. The governing electromechanical equations are derived using the constitutive relations of piezoelectric materials and Maxwell’s equations. To model the host system with piezoelectric material as both a complete shell and a panel, and to represent the piezoelectric material as a patch, the two-dimensional Generalized Differential Quadrature (2D–GDQ) method is employed. Utilizing of the 2D–GDQ approach is essential for accurately capturing variations in both the axial and circumferential directions, which cannot be achieved with a one-dimensional formulation. The natural frequencies of the shell and panel with piezoelectric patches are computed under various electrical and mechanical boundary conditions. The accuracy of proposed model and numerical approach is validated through comparisons with published results and finite element simulations conducted in Abaqus software. Furthermore, the study examines the influence of key geometric parameters—including the radius and length of the host panel, as well as the thicknesses of the piezoelectric patch and the host shell—on the natural frequencies.
Motazedian et al. (Tue,) studied this question.