当前位置: X-MOL 学术J. Vib. Control › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Galerkin–Ivanov transformation for nonsmooth modeling of vibro-impacts in continuous structures
Journal of Vibration and Control ( IF 2.8 ) Pub Date : 2020-07-24 , DOI: 10.1177/1077546320945441
Surya Samukham 1 , S. N. Khaderi 1 , C. P. Vyasarayani 1
Affiliation  

This work deals with the modeling of nonsmooth vibro-impact motion of a continuous structure against a rigid distributed obstacle. Galerkin’s approach is used to approximate the solutions of the governing partial differential equations of the structure, which results in a system of ordinary differential equations. When these ordinary differential equations are subjected to unilateral constraints and velocity jump conditions, one must use an event detection algorithm to calculate the time of impact accurately. Event detection in the presence of multiple simultaneous impacts is a computationally demanding task. Ivanov (Ivanov A 1993 “Analytical methods in the theory of vibro-impact systems”. Journal of Applied Mathematics and Mechanics 57(2): pp. 221–236.) proposed a nonsmooth transformation for a vibro-impacting multi-degree-of-freedom system subjected to a single unilateral constraint. This transformation eliminates the unilateral constraints from the problem and, therefore, no event detection is required during numerical integration. This nonsmooth transformation leads to sign function nonlinearities in the equations of motion. However, they can be easily accounted for during numerical integration. Ivanov used his transformation to make analytical calculations for the stability and bifurcations of vibro-impacting motions; however, he did not explore its application for simulating distributed collisions in spatially continuous structures. We adopt Ivanov’s transformation to deal with multiple unilateral constraints in spatially continuous structures. Also, imposing the velocity jump conditions exactly in the modal coordinates is nontrivial and challenging. Therefore, in this work, we use a modal-physical transformation to convert the system from modal to physical coordinates on a spatially discretized grid. We then apply Ivanov’s transformation on the physical system to simulate the vibro-impact motion of the structure. The developed method is demonstrated by modeling the distributed collision of a nonlinear string against a rigid distributed surface. For validation, we compare our results with the well-known penalty approach.



中文翻译:

Galerkin–Ivanov变换用于连续结构中振动冲击的非平滑建模

这项工作涉及连续结构对刚性分布障碍物的非光滑振动冲击运动的建模。Galerkin的方法用于近似控制结构的部分偏微分方程的解,从而形成一个常微分方程组。当这些常微分方程受到单边约束和速度跳跃条件时,必须使用一种事件检测算法来准确计算碰撞时间。在存在多个同时影响的情况下进行事件检测是一项计算量巨大的任务。Ivanov(Ivanov A 1993,“振动冲击系统理论中的分析方法”。应用数学和力学杂志 57(2):第221-236页)提出了一个受单个单边约束的,具有振动影响的多自由度系统的非光滑变换。这种变换消除了问题的单方面约束,因此,在数值积分期间不需要事件检测。这种不平滑的变换导致运动方程中的符号函数非线性。但是,它们可以在数值积分过程中轻松解决。伊万诺夫(Ivanov)利用他的变换对振动运动的稳定性和分叉进行了分析计算。但是,他没有探索其在模拟空间连续结构中的分布式碰撞中的应用。我们采用Ivanov变换来处理空间连续结构中的多个单边约束。也,将速度跳跃条件精确地施加在模态坐标中是不平凡且具有挑战性的。因此,在这项工作中,我们使用模态-物理变换将系统从模态转换为空间离散网格上的物理坐标。然后,我们在物理系统上应用Ivanov变换来模拟结构的振动冲击运动。通过对非线性弦与刚性分布表面的分布碰撞进行建模来证明所开发的方法。为了进行验证,我们将结果与众所周知的惩罚方法进行了比较。然后,我们在物理系统上应用Ivanov变换来模拟结构的振动冲击运动。通过对非线性弦与刚性分布表面的分布碰撞进行建模来证明所开发的方法。为了进行验证,我们将结果与众所周知的惩罚方法进行了比较。然后,我们在物理系统上应用Ivanov变换来模拟结构的振动冲击运动。通过对非线性弦与刚性分布表面的分布碰撞进行建模来证明所开发的方法。为了进行验证,我们将我们的结果与众所周知的惩罚方法进行了比较。

更新日期:2020-07-24
down
wechat
bug