Nonlinear forced vibrations of functionally graded piezoelectric cylindrical shells under electric-thermo-mechanical loads

This paper develops a new solution approach to solve nonlinear forced vibrations of functionally graded (FG) piezoelectric shells in multi-physics fields. The FG piezoelectric shells are subjected to electric-thermo-mechanical loads, and the effect of micro-voids is considered here. Motion equations are obtained by using Hamilton's principle, and combining with the Donnell nonlinear shallow shell theory. Afterwards, a new method combining multi-mode Galerkin scheme and Pseudo-arclength continuation method is used to solve the nonlinear multiple internal resonances and bifurcations of the multi-degree-of-freedom systems. The novel feature of this approach is that it can efficiently obtain the unstable solution and tackle the difficult problems in mathematics encountered during formulation. The results show that the external applied voltage, temperature change, external excitation, power-law exponent, and porosity volume fraction play important roles on nonlinear vibration response and bifurcation analysis of FG piezoelectric shells with micro-voids.

Automated summary

This paper presents a new solution approach to address the nonlinear forced vibrations of functionally graded piezoelectric shells in multi-physics fields, considering the effects of micro-voids. By utilizing Hamilton's principle and the Donnell nonlinear shallow shell theory, motion equations are derived, and a novel method combining multi-mode Galerkin scheme and Pseudo-arclength continuation method is employed to solve the nonlinear multiple internal resonances and bifurcations of the systems with multiple degrees of freedom.