Accepted: 7 May 2024 | Qiliang Wu, Shuaichao Wang, Minghui Yao, Yan Niu, Cong Wang
This paper analyzes the nonlinear dynamic responses of a cantilevered three-layer microplate with geometric imperfections. The partial differential equations for the microplate are derived using modified couple stress theory, geometrically nonlinear von Karman equations, and Reddy’s first-order shear deformation plate theory. The equations are discretized using Galerkin’s technique, and the model is validated against published data. The frequency response function of the second-order motion equation is derived using a multi-scale method to preserve the quadratic term caused by defects. The study reveals how in-plane excitation, micro-scale effects, imperfect amplitude, and transverse excitation influence the amplitude-frequency response characteristics. Numerical examples demonstrate that variations in transverse excitation can lead to periodic, multi-periodic, and chaotic motions. The research highlights the unique deformation behavior of microstructures due to their small dimensions and the importance of considering geometric imperfections in the analysis of microplate dynamics.This paper analyzes the nonlinear dynamic responses of a cantilevered three-layer microplate with geometric imperfections. The partial differential equations for the microplate are derived using modified couple stress theory, geometrically nonlinear von Karman equations, and Reddy’s first-order shear deformation plate theory. The equations are discretized using Galerkin’s technique, and the model is validated against published data. The frequency response function of the second-order motion equation is derived using a multi-scale method to preserve the quadratic term caused by defects. The study reveals how in-plane excitation, micro-scale effects, imperfect amplitude, and transverse excitation influence the amplitude-frequency response characteristics. Numerical examples demonstrate that variations in transverse excitation can lead to periodic, multi-periodic, and chaotic motions. The research highlights the unique deformation behavior of microstructures due to their small dimensions and the importance of considering geometric imperfections in the analysis of microplate dynamics.