基于有限元法的一维球链中高非线性孤立波传播特性

Finite Element Simulation of Highly Nonlinear Solitary Waves in One-dimensional Granular Chain

为发展一种基于高非线性孤立波技术的无损检测新方法,仿真研究了一维球链中高非线性孤立波的传播特性.高非线性孤立波是一种可在高非线性系统中形成和传播的机械波,例如一维球形颗粒链等.利用Abaqus仿真平台,建立了含21个球形颗粒的一维颗粒链模型.研究网格划分对于有限元计算结果的影响,选取最优网格划分等级;采用接触对算法,仿真分析了孤立波的形成、传播过程.提取不同颗粒接触区域的力-时间变化曲线,计算得出撞击速度为0.313 m/s情况下的孤立波波速为562 m/s,与相同条件下的理论波速相对误差为3.3%;当孤立波从一维球形颗粒链传到待测圆柱表面时将发生反射行为,并形成反射孤立波.利用有限元法分析反射孤立波信号特征参数与待测试样弹性常数间的关系,为基于非线性孤立波的无损检测技术提供指导.

To develop a new nondestructive test method based on high nonlinear solitary waves（ HNSWs）,the propagation properties of HNSWs in one-dimensional granular chain were simulated.HNSWs can form and travel in highly nonlinear systems,such as one-dimensional granular chain. In the present study,a granular chain which was composed of twenty-one spherical particles and a coupled cylinder were modeled in the commercial software of Abaqus. The influence of mesh setup on the results of finite element calculation was discussed,and the optimal meshing grade was selected. The propagation and reflection behavior of the HNSWs in the coupled system were simulated by using the contact pair algorithm. The formation of HNSWs was discussed and the speed of the HNSWs was determined by using the extracted time-force profiles at the contact points. The good agreement between the simulated and theoretical speed verifies the feasibility of the proposed finite element simulation method. The reflection of HNSWs at the particle-cylinder interface can also be simulated and observed as the reflected solitary wave signal. Having the developed model,the characteristics of the reflected solitary wave signal can be investigated for specific cases to develop NDE method.