Static bending and forced vibration analyses of a piezoelectric semiconductor cylindrical shell within first-order shear deformation theory

This paper examines the mechanically induced electric potential and charge redistribution in a piezoelectric semiconductor cylindrical shell employing first-order shear deformation theory. The two-dimensional governing equations and corresponding boundary conditions are simultaneously derived through a principle of virtual work method and the fundamental lemma of the calculus of variation. For the application of electronic devices, static bending and forced vibration analyses of an open cylindrical shell under locally distributed normal forces are analytically solved with the derived theoretical model. The effects of doping level on electric potentials and mechanical displacements are presented. An interesting result shows that doping levels can alter the peak position of the zeroth-order electric potential. In addition, the first three order natural frequencies of the shell under time-harmonic load are identified, and the doping level is found to have an inhibiting effect on the first natural frequency. All the numerical results are beneficial for optimizing the design and performance of cylindrical shell-shaped sensors and energy harvesters.