This paper presents a new numerical method to solve the non-linear constitutive equations of viscoelastic string with variable fractional order model. Firstly, the non-linear constitutive equation of the string is established based on the variable fractional viscoelastic model. Secondly, non-linear constitutive equation of the string is transformed into a matrix equation by using Bernstein polynomials, which can greatly simplify the solving process. Then the matrix equation is discretized and solved to obtain the numerical solutions. Finally, numerical results of viscoelastic string show the effect of the axial tension and axial velocity on its displacement, velocity and acceleration. It also indicates that how dynamic behaviours are affected by external force excitation. In addition, the proposed algorithm shows enormous potentials for solving the problem of high precision dynamics with the variable fractional order model.

本文提出了一种用变分数阶模型求解粘弹性弦非线性本构方程的新数值方法。首先，基于可变分数粘弹性模型建立了弦的非线性本构方程。其次，利用伯恩斯坦多项式将弦的非线性本构方程转化为矩阵方程，可以大大简化求解过程。然后对矩阵方程进行离散求解，得到数值解。最后，粘弹性弦的数值结果显示了轴向张力和轴向速度对其位移、速度和加速度的影响。它还表明动态行为如何受到外力激励的影响。此外，