Nonlinear dynamics and parameter control for metamaterial plate with negative Poisson’s ratio

Abstract

The metamaterial with negative Poison s ratio is widely used due to its special mechanical and physical properties. Based on the theory of periodic solution and bifurcation of nonlinear dynamics, we mainly focus on the nonlinear vibration behaviors and parameter control of a simply supported concave hexagonal composite sandwich plate with negative Poisson s ratio in auxetic honeycombs subjected to in-plane and transverse excitation. The Melnikov function is improved by introducing the curvilinear coordinate frame and Poincare map to detect the existence and number of the periodic solutions. The effects of the forcing excitation coefficient on nonlinear dynamics as well as the parameter control conditions are presented. Numerical method is performed to obtain the phase portraits of the number and corresponding positions of multiple periodic orbits.