【目的】为了理解含中间支撑约束轴向移动梁的非线性振动响应特征。【方法】基于Hamilton原理建立了系统的动力学方程,并使用伽辽金法将运动方程离散为非线性常微分方程。将改进的弧长延拓法与增量谐波平衡法结合,求解系统的动力学方程,并分析了系统在不同参数下的动力学响应特征。【结果】研究表明,系统响应整体上呈现硬弹簧特征。支撑弹簧对轴向移动梁有重要的影响。此外,当轴向移动速度在一定范围内,系统存在内共振,系统的响应呈现更加复杂的响应特征。

【Purposes】 This work is conducted to understand the nonlinear vibration response  characteristics of axially moving beams with intermediate support constraints. 【Methods】The dy⁃ namic equation of the system was established on the basis of Hamilton principle, and the motion equa⁃ tion was discretized into a nonlinear ordinary differential equation by using the Galerkin method. By  combining the improved arclength extension method with the incremental harmonic balance method,  the dynamic equations of the system were solved, and the dynamic response characteristics of the sys⁃ tem under different parameters were analyzed. 【Findings】 It is shown that the overall system re⁃ sponse exhibits a hard spring characteristic. The support spring has a significant impact on the dynam⁃ ics of the axially moving beam. In addition, when the axial movement speed is within a certain range,  the system exhibits internal resonance, and the system shows more complex response characteristics.