Nonlinear dynamics of three-layer microplates: simultaneous presence of the micro-scale and imperfect effects

Nonlinear dynamics of three-layer microplates: simultaneous presence of the micro-scale and imperfect effects

28 May 2024 | Qiliang Wu, Shuaichao Wang, Minghui Yao, Yan Niu, Cong Wang
This paper presents an analysis of the nonlinear dynamic responses of a cantilevered three-layer microplate with geometric imperfections. The governing equations are derived using the modified couple stress theory, the geometrically nonlinear von Karman equations, and Reddy's first-order shear deformation plate theory. The nonlinear partial differential equations are discretized using the Galerkin technique. The model is validated against published data, showing good agreement. The frequency response function of the second-order motion equation is derived using the multi-scale method to preserve the quadratic term caused by defects. The presence of defects leads to an asymmetric shape, altering the system's stiffness characteristics. The study reveals how in-plane excitation, micro-scale effects, imperfect amplitude, and transverse excitation influence the amplitude-frequency response characteristics. Numerical examples show that variations in transverse excitation can lead to periodic, multi-periodic, and chaotic motions. The study highlights the importance of considering micro-scale effects and geometric imperfections in the analysis of microstructures. The research also discusses the application of various theories and methods, including the modified couple stress theory, to analyze the dynamic behavior of microplates. The study emphasizes the need for accurate modeling of microstructures, considering their unique deformation behavior, which is size-dependent and cannot be accurately predicted by classical continuum theory. The results demonstrate the effectiveness of the proposed method in analyzing the dynamic behavior of microplates with geometric imperfections. The study provides a solid foundation for the practical design and implementation of cantilever laminated microplate structures.This paper presents an analysis of the nonlinear dynamic responses of a cantilevered three-layer microplate with geometric imperfections. The governing equations are derived using the modified couple stress theory, the geometrically nonlinear von Karman equations, and Reddy's first-order shear deformation plate theory. The nonlinear partial differential equations are discretized using the Galerkin technique. The model is validated against published data, showing good agreement. The frequency response function of the second-order motion equation is derived using the multi-scale method to preserve the quadratic term caused by defects. The presence of defects leads to an asymmetric shape, altering the system's stiffness characteristics. The study reveals how in-plane excitation, micro-scale effects, imperfect amplitude, and transverse excitation influence the amplitude-frequency response characteristics. Numerical examples show that variations in transverse excitation can lead to periodic, multi-periodic, and chaotic motions. The study highlights the importance of considering micro-scale effects and geometric imperfections in the analysis of microstructures. The research also discusses the application of various theories and methods, including the modified couple stress theory, to analyze the dynamic behavior of microplates. The study emphasizes the need for accurate modeling of microstructures, considering their unique deformation behavior, which is size-dependent and cannot be accurately predicted by classical continuum theory. The results demonstrate the effectiveness of the proposed method in analyzing the dynamic behavior of microplates with geometric imperfections. The study provides a solid foundation for the practical design and implementation of cantilever laminated microplate structures.
Reach us at info@study.space