基于应变修正的二维缆索动力学建模改进

Improvement of two-dimensional dynamic modeling of cable based on strain modification

本文基于非线性连续介质力学思想和微分几何中的曲线理论,综合考虑Perkins模型的非线性应变和Howell模型的动态曲率,在更新的拉格朗日格式下,基于当前构形建立了缆索结构包含动态曲率和大应变的平面动力学方程组.运用无量纲参数分析化简了剪力的表达式,在平面动力学方程组中补充非线性几何方程与相对转角方程,形成了修正的Howell模型.通过分析拉力、剪力项系数,说明原Howell模型与修正模型的差别.通过算例分析,说明了修正Howell模型在计算精度和计算效率方面的优越性.

In this paper,based on the nonlinear continuum mechanics and curve theory in differential geometry,we comprehensively consider the nonlinear strain of Perkins’model and the dynamic curvature of Howell’s model for model establishment.Under the updated Lagrangian formulation,we establish the plane dynamic equations of the cable structure,including dynamic curvature and large strain based on the current configuration.The expression of shear force is simplified using dimensionless parameter analysis,and the nonlinear geometric equation and the relative rotation angle equation are supplemented in the plane dynamic equations to form the modified Howell model.We illustrate the difference between the original and modified Howell model by analyzing the tension and shear coefficients.Moreover,we illustrate the superiority of the modified Howell model in terms of computational accuracy and efficiency through examples.