A coupled dynamic system consisting of a supporting beam structure and multiple passing rigid bodies is seen in various engineering applications. The dynamic response of such a coupled system is quite different from that of the beam structure subject to moving loads or moving oscillators. The dynamic interactions between the beam and moving rigid bodies are complicated, mainly because of the time-varying number and locations of contact points between the beam and bodies. Due to lack of an efficient modeling and solution technique, previous studies on these coupled systems have been limited to a beam carrying one or a few moving rigid bodies. As such, dynamic interactions between a supporting structure and arbitrarily many moving rigid bodies have not been well investigated, and parametric resonance induced by a sequence of moving rigid bodies, which has important engineering implications, is missed. In this paper, a new semi-analytical method for modeling and analysis of the above-mentioned coupled systems is developed. The method is based on an extended solution domain, by which the number of degrees of freedom of a coupled system is fixed regardless of the number of contact points between the beam and moving rigid bodies at any given time. This feature allows simple and concise description of flexible–rigid body interactions in modeling, and easy and effective implementation of numerical algorithms in solution. The proposed method provides a useful platform for thorough study of flexible–rigid body interactions and parametric resonance for coupled beam–moving rigid body systems. The accuracy and efficiency of the proposed method in computation is demonstrated in several examples.

中文翻译：

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连续运动刚体激发的梁结构的动力响应

在各种工程应用中都可以看到由支撑梁结构和多个通过的刚体组成的耦合动力系统。这种耦合系统的动态响应与受到移动载荷或移动振荡器的梁结构的动态响应有很大不同。梁与运动刚体之间的动力相互作用是复杂的，主要是由于梁与刚体之间接触点的数量和位置随时间变化。由于缺乏有效的建模和求解技术，以前对这些耦合系统的研究仅限于承载一个或几个移动刚体的梁。因此，支撑结构与任意多个移动刚体之间的动态相互作用尚未得到很好的研究，以及由一系列移动刚体引起的参数共振，错过了具有重要工程意义的内容。在本文中，开发了一种新的半解析方法，用于对上述耦合系统进行建模和分析。该方法基于扩展的解域，通过该域，耦合系统的自由度数是固定的，而与在任何给定时间梁和移动刚体之间的接触点数无关。此功能允许在建模中简单而简洁地描述刚体-刚体相互作用，并在求解中轻松有效地实现数值算法。所提出的方法为深入研究耦合梁移动刚体系统的柔刚体相互作用和参数共振提供了一个有用的平台。在几个例子中证明了所提出的方法在计算中的准确性和效率。