https://doi.org/10.1140/epjp/s13360-024-05255-3
Regular Article
Nonlinear dynamics of three-layer microplates: simultaneous presence of the micro-scale and imperfect effects
1
School of Aeronautics and Astronautics, Tiangong University, 300387, Tianjin, People’s Republic of China
2
School of Control Science and Engineering, Tianjin Key Laboratory of Intelligent Control of Electrical Equipment, Tiangong University, 300387, Tianjin, People’s Republic of China
Received:
5
January
2024
Accepted:
7
May
2024
Published online:
28
May
2024
This paper presents an analysis of nonlinear dynamic responses of a cantilevered three-layer microplate with geometric imperfections. The partial differential equations for such a microplate with geometric imperfections are derived using the modified couple stress theory, the geometrically nonlinear von Karman equations, and Reddy's first-order shear deformation plate theory. Discretization of the nonlinear partial differential equations is performed using the Galerkin's technique. The proposed model is compared with the published model data, and the results show good agreement, which further proves the validity of the model. Considering the internal resonance of the system at 1:2, the frequency response function of the second-order motion equation is derived by multi-scale method in order to preserve the quadratic term caused by defects. The existence of defects will cause the model to show an asymmetric shape, which will cause the stiffness characteristics of the system itself to change. It is revealed how the in-plane excitation, micro-scale effect, imperfect amplitude, and transverse excitation all influence the amplitude-frequency response characteristics. Numerical examples demonstrate that variations in transverse excitation can lead to periodic, multi-periodic, and chaotic motions.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
