Nonlinear vibrations of fractional viscoelastic PET membranes subjected to tangential follower force

Abstract

Nonlinear forced vibrations of simply supported viscoelastic Polyethylene Terephthalate (PET) membranes subjected to a harmonic excitation and tangential follower force are investigated in this paper. The consideration of vibration systems under follower force requires special attention to the modeling of non-conservative force and its influence on nonlinear analysis. Herein, a fractional Kelvin-Voigt Hamilton-based framework accounting for the viscoelastic PET membrane is developed. Based on the Hamilton principle for the non-conservative system, the mathematical modeling of viscoelastic PET membrane taking into account non-conservative force and geometric nonlinearity is formulated, and the derived equations are discretized via the Galerkin schemes. A technique of multiple scales is employed to numerically acquire the frequency–response curves with different system configurations. Numerical investigations are conducted to analyze the effects of tangential follower force, viscous coefficient, as well as fractional order on the dynamic stability of the considered structure. Further ramifications of the present study point to the paramount importance of tangential follower force and an accurate viscoelasticity model on the dynamic behaviors of the viscoelastic structures.