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.

本文分别为粘弹性板的建模和数值模拟提供了新的有效方法。粘弹性板采用可变分数阶导数模型建模，拟合效果更好，首次采用位移切比雪夫小波算法直接在时域进行数值分析。建立了具有三个自变量的控制方程。通过算例的收敛性分析和误差估计，验证了所提算法的可行性和准确性。在不同条件下，直接在时域内采用位移切比雪夫小波算法对板的三元变量分数阶微分方程进行数值求解。分析了板在不同载荷、加载时间和温度下的振动。还计算分析了相同载荷下两种材料板的应力数值解。板的位移随着载荷、加载时间和温度的增加而增加。PET板的抗弯性能优于聚脲板。这些结果与现有的参考文献和实际做法是一致的。因此，可变分数模型和移位切比雪夫小波算法对于板的研究是准确的。它们可以应用于工程中的复杂问题。所得结论可为工程中承重结构的防护与设计提供理论依据。PET板的抗弯性能优于聚脲板。这些结果与现有的参考文献和实际做法是一致的。因此，可变分数模型和移位切比雪夫小波算法对于板的研究是准确的。它们可以应用于工程中的复杂问题。所得结论可为工程中承重结构的防护与设计提供理论依据。PET板的抗弯性能优于聚脲板。这些结果与现有的参考文献和实际做法是一致的。因此，可变分数模型和移位切比雪夫小波算法对于板的研究是准确的。它们可以应用于工程中的复杂问题。所得结论可为工程中承重结构的防护与设计提供理论依据。