Dynamic Buckling Analysis of Thin Film/Polydimethylsiloxane Substrate Structures in Curved State with Finite Thickness

Curved sensors hold significant positions in various fields of modern science and technology, such as medical care, soft robotics, and electronic devices. Meanwhile, flexible electronic devices with film/polydimethylsiloxane substrate structures have been widely applied in the configuration design and performance enhancement of sensors. It is essential to consider the dynamic buckling behavior of film/substrate structures under bending conditions for the optimization of sensor functions. In this study, the dynamic behaviors of thin film/substrate structures with finite thickness in the curved state are investigated. Firstly, the dynamic equations considering damping and external excitation are established based on the principle of minimum energy and the Lagrange function. Secondly, the dynamic responses under different parameters are analyzed. Finally, the effects of the frequency of external excitation, pre-strain, the amplitude of external excitation strain, and the Young's modulus and thickness of the substrate on the critical value of chaos occurrence are discussed respectively. This study is aimed at providing novel insights for the design of curved sensors based on thin film/substrate structures.