Multi-field coupling and vibration analysis of a piezoelectric semiconductor cylindrical shell

In this paper, the free and forced vibration behaviors of a piezoelectric semiconductor (PS) cylindrical shell are investigated based on the first order shear deformation theory. According to the constitutive equation as well as geometric relationship, the kinetic energy, strain energy and virtual work of the PS cylindrical shell are obtained. Furthermore, the vibration governing equations of the system are derived by means of Hamilton's principle, and the analytical solutions are acquired for the simply supported PS cylindrical shell. Through numerical examples, the effects of the initial electron concentration, circumferential wave number, geometric parameter and excitation frequency on the natural frequency, damping characteristic, vibration amplitude and induced electric potential of the PS cylindrical shell are discussed. The multi-field coupling characteristic among deformation, polarization and carrier is revealed. The main innovation of the manuscript is that the maximum radial displacement and induced electric potential of the PS cylindrical shell can be effectively controlled by doping different initial electron concentrations, and the damping characteristic of the system is obviously size-dependent.