Variable fractional modeling and vibration analysis of variable-thickness viscoelastic circular plate

Abstract

In this paper, a variable fractional derivative model (VFDM) is used to model the viscoelastic circular plate whose thickness varies exponentially. Based on the VFDM, a ternary variable fractional differential equation of viscoelastic circular plate is established. The shifted Chebyshev polynomials (SCPs) algorithm is introduced to numerically solve the complex equation directly in time domain. The effectiveness of proposed SCPs algorithm is verified by convergence analysis. Then the dynamic responses of viscoelastic circular plate are researched under different loads, radius, thickness parameters, boundary conditions and viscoelastic materials by SCPs algorithm. The displacement of circular plate increases with the increasing load. The vibration can be reduced by increasing the thickness of plate, reducing plate area or strengthening the restraint on plate. The bending resistance of polyethylene terephthalate (PET) plate is better than polyurea. These results are consistent with the results of literatures. Therefore, the proposed model and algorithm are correct and sensitive in the numerical simulation of viscoelastic circular plate with different conditions.