Vibration analysis of variable fractional viscoelastic plate based on shifted Chebyshev wavelets algorithm

Abstract

In this paper, new and effective methods are provided for modeling and numerical simulation of viscoelastic plate, respectively. Viscoelastic plate is modeled by a variable fractional derivative model with better fitting effect and is numerically analyzed directly in time domain using shifted Chebyshev wavelets algorithm for the first time. A governing equation with three independent variables is established. The feasibility and accuracy of proposed algorithm are verified by convergence analysis and error estimations of mathematical example. Under different conditions, the ternary variable fractional differential equation of plate is solved numerically by shifted Chebyshev wavelets algorithm directly in time domain. The vibrations of plate are analyzed under different loads, loading times and temperatures. Numerical solutions for the stress of plate with two materials are also calculated and analyzed under the same load. The displacement of plate increases with increasing load, loading time and temperature. The bending resistance of PET plate is better than that of polyurea plate. These results are consistent with the existing references and actual practice. Therefore, the variable fractional model and shifted Chebyshev wavelets algorithm are accurate for the study of plate. They can be applied to complex problems in engineering. All obtained conclusions can provide theoretical basis for the protection and design of load-bearing structures in engineering.