Kinetic Analysis of Fractional Viscoelastic Films Based on Shifting Legendre Polynomials

In this paper, the variable fractional derivative model was used to simulate the structure of viscoelastic polyethylene terephthalate (PET) films. the shift Legendre polynomial algorithm is used to directly solve the equation of motion in the time domain, and the nonlinear dynamic response of the fractional viscoelastic film is reliably estimated. Numerical examples demonstrate the reliability and accuracy of the proposed strategy, and the displacement of thin films with different aspect ratios under simple harmonic loading is numerically simulated.