Variational fractional-order modeling of viscoelastic axially moving plates and vibration simulation

Abstract

Based on the thin plate theory and D’Alembert’s principle to establish the equilibrium equation for viscoelastic axially moving plates, this paper establishes the ternary governing equation of variable fractional order for viscoelastic axially moving plates by using a variable fractional order constitutive relationship for viscoelastic materials. Shifted Chebyshev wavelets are introduced for approximating the deflection function, and numerical solutions for the governing equations are given. The effectiveness and accuracy of the algorithm in this paper is illustrated by convergence analysis, error correction and numerical examples. Finally, the algorithm is used to simulate the vibration of axially moving plates with different moving speeds and different boundary conditions. Meanwhile, Gaussian white noise was introduced to investigate the vibration of the viscoelastic axially moving plate under pure noise environment, simple harmonic load-same direction noise environment and simple harmonic load-opposite direction noise environment, respectively. And the vibration comparison of PP material plate and LLDPE material plate is also carried out. The above research conclusions are consistent with the existing literature, indicating that algorithm proposed by this paper is applicable to numerical simulation and research on viscoelastic axially moving plates.