Structural stability enhancement by nonlinear geometry design and piezoelectric layers

Abstract

Vibration and stability analysis of nonlinearly tapered cone beams coupled with a piezoelectric layer under compressive axial load is conducted using a new semi-theoretical model based on the Adomian decomposition method and a modified mathematical procedure. The method is applied to tapered structures with perfectly surface-bonded piezoelectric layers and general boundary conditions to analytically derive the natural frequencies and mode shape functions for flutter and buckling analysis. Furthermore, from the optimum structural design perspective, the effects of follower force, geometrical tapering ratio, boundary condition, and applied voltage on piezoelectric layers on the structural stability are thoroughly studied and presented. Simulation results show that the stability of the beam can be noticeably enhanced by the external voltage because of a pair of tensile loads locally induced by the piezoelectric effect. Moreover, for certain boundary conditions and applied voltages, the nonlinear tapered design has much greater buckling and flutter capacities than does the uniform beam. Consequently, the ideal structural design for effective stability enhancement can be reached efficiently.