Dynamic Behaviors of Postbuckled Thin Film on Flexible Substrates Considering Viscoelastic Effects

Stretchable electronic systems based on controllable compressive buckling can be further endowed with superior compliance and stretchability. However, such systems are usually restrained by the interference from different loads in practical applications, so it is desirable to study their dynamic behaviors. In this article, an analytical model is developed on the linear free vibrations of a buckled thin film attached to a flexible substrate, whose results can be verified by the finite element analysis (FEA). In the model, the film is considered as an Euler-Bernoulli beam, and the substrate is assumed as a Pasternak foundation with Kelvin viscoelasticity. The natural frequencies and their corresponding vibration modes of the buckled film with the substrate are obtained. The results indicate that the increases of stiffness and damping of the substrate have negative effects on the natural frequencies. The damping influences the low-order modes a lot but not the high-order modes. This study may provide some suggestions for the dynamic design of buckled thin films on flexible substrates. For example, the controllable vibration attenuation can be achieved by choosing the substrate with appropriate viscoelasticity.