Electro-mechanical vibration characteristics of piezoelectric nano shells

This paper presents the application of higher-order shear deformation theory and nonlocal elasticity theory to electro-mechanical vibration analysis of a doubly curved piezoelectric nano shell resting on Pasternak's foundation. The piezoelectric doubly curved nanoshell is subjected to initial electro-mechanical loads. Effect of initial electro-mechanical loads is contributed in external works. Size effects are captured by nonlocal elasticity theory and Hamilton's principle is employed to derive the equation of motion in terms of three displacements of the middle surface, two rotational components and one electric potential. The main novelty of this paper is investigating concurrent effect of initial electro-mechanical loads, higher-order shear deformation theory and size dependent theory on the free vibration responses of doubly curved piezoelectric nano shell with various boundary conditions. The electro-mechanical vibration response of the doubly curved piezoelectric nano shell is investigated using an analytical method in terms of various parameters such as two opening angles, small scale parameter, spring and shear parameters of foundation and initial electric potential. It is concluded that increasing the nonlocal parameter leads to decrease of the natural frequencies of shell while increasing the applied electric potential increases the natural frequencies.