Primary and secondary resonance responses of fractional viscoelastic PET membranes

Abstract

This paper considers nonlinear vibration of fractional viscoelastic Polyethylene Terephthalate (PET) membranes subjected to external excitation. Particular attention has been paid to the effects of parameters associated with the fractional model on the primary and secondary resonance responses. Here, the fractional Kelvin–Voigt constitutive relation is adopted to describe the viscoelastic material. Based on von-Karman theory and Newton’s second law, the governing equation is derived. The Galerkin technique is utilized to discretize the nonlinear equation of motion. The multiple-scale method is employed to assess the forced responses of the membrane system under external excitation. Numerical results reveal that the fractional viscoelastic model strongly affects the resonance response of membranes. In this regard, these results offer insight into further study on the vibration characteristics of fractional viscoelastic membranes and also determine the stable operating regions of the moving system to avoid divergent instability in the fabrication of flexible electronics.