分数阶粘弹性Euler-Bernoulli梁的数值分析

Numerical analysis of fractional viscoelastic Euler-Bernoulli beams

为探究时域中分数阶粘弹性Euler-Bernoulli梁的控制方程数值解的问题,提出基于移位Chebyshev多项式的有效数值算法.基于分数阶粘弹性Euler-Bernoulli梁的控制方程,采用多项式逼近方法和算子矩阵技术将控制方程转化为矩阵乘积的形式,利用配点法对变量进行离散化将原问题转化为代数方程组进而在时域内得到控制方程的数值解.研究结果表明:粘弹性材料丁基B252的抗弯性能较聚丁二烯更好,其结果与实际相符,进一步验证了本文算法的有效性和准确性.研究结论初步突破在时域内建立并求解分数阶粘弹性Euler-Bernoulli梁的分数阶模型,为阻尼材料的研究、开发和性能预测提供理论依据.

In order to investigate the numerical solution of the control equation of the fractional viscoelastic Euler-Bernoulli beam in the time domain,an effective numerical algorithm based on shifted Chebyshev polynomials is proposed.Based on the control equation of the fractional viscoelastic Euler-Bernoulli beam,the polynomial approximation method and the operator matrix technique are used to transform the control equation into the form of matrix product.By using the method of collocation to discretize variables,the original problem is transformed into algebraic equations,and then the numerical solution of control equations is obtained in the time domain.The results show that the bending resistance of the viscoelastic material Butyl b252 is better than that of Polybutadiene,and the results are consistent with the actual situation,which further verifies the effectiveness and accuracy of the algorithm proposed in this paper.The research results break through the establishment and solution of fractional order viscoelastic Euler-Bernoulli beam in time domain.It provides theoretical basis for the research,development and performance prediction of damping materials.