Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton’s principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.

中文翻译：

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梁结构的非线性耦合运动荷载激励动力学

本文研究的是梁质量系统中由于运动载荷引起的非线性耦合动力学的第一篇论文。恒定值的负载会激发束质量系统，在束质量系统上，束质量系统上的位置会定期更改。通过虚拟功公式包括移动负载的能量贡献。制定了质量与梁的动能以及偏转后存储在梁中的能量。汉密尔顿原理给出了在移动载荷下横梁/纵梁耦合形式的梁质量系统的非线性方程。基于加权残差的离散化提供了20个自由度，该自由度通过连续/时间积分与Floquet理论技术进行数值积分。研究了时域，频域和空间域的共振动力学。正如我们将看到，对于某些束质量结构参数以及行波，存在圆环分叉。对问题的简单线性版本进行有限元分析，以进行某种程度的扩展验证。