Dynamical responses of variable generatrix profile and thickness ceramic-matrix composite shells under electro-thermo-mechanical effects

In this paper, new structures of shells have been proposed with complex profiles and thicknesses varying through the length direction subjected to a thermal environment. The inner and outer surfaces of the shells are bonded to the piezoelectric actuators with changes of various voltages. The nonlinear motion equations of variable generatrix profile and thickness (VGPT) shells are solved to investigate the nonlinear vibration and chaotic responses using the theory of elasticity and Von Karman-Donnell’s geometrical nonlinearity assumption. Four kinds of VGPT shells are combined by two types of complex profiles and two patterns of thickness distribution. The used materials are made of Silicon carbide (SiC) and Borosilicate. Galerkin’s method is applied to solve the systems of differential equations and then the fundamental frequencies and nonlinear dynamic behaviors can be found. The effects of material (coefficient k), geometrical parameters, thickness, piezoelectric layers, and thermal environment on the dynamic responses of VGPT shells are examined and presented in tables and graphs. •The shells that vary in both genetrix profile and thickness are investigated.•The used materials are ceramic-matrix composite including: Silicon carbide (SiC) and Borosilicate.•The nonlinear dynamical and chaotic behaviors of new structures are scrutinized.