This work focuses on the revelation of nonlinear characteristics of a hinged–clamped beam moving with pulsating speed. Cubic geometric nonlinearity, viscous damping due to intervening medium, and viscoelastic material damping are considered in the governing equation of motion. Parametric excitation is induced in the system due to pulsating speed amid 3:1 internal resonance between the first two modes. A perturbation technique-direct method of multiple scales is applied to solve the problem. Nonlinear features like various stability and bifurcation phenomena are extracted by applying a continuation algorithm. Trivial state stability plot and the impacts of viscous and material damping have been studied. The consequence of alterations of the amplitude of pulsating speed constituent, internal frequency detuning parameter, axial stiffness, and parametric detuning parameter on the vibration responses have been analyzed in detail. The analytic-numeric approach reveals rich and interesting nonlinear phenomena under united parametric and internal resonances in the study of the hinged–clamped beam that are not available in the existing literature.

中文翻译：

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以脉动速度运动并经受内共振的铰接夹紧梁的非线性振动分析

这项工作的重点是揭示以脉动速度移动的铰接钳位梁的非线性特性。在运动控制方程中考虑了三次几何非线性、由于中间介质引起的粘性阻尼和粘弹性材料阻尼。由于前两种模式之间的 3:1 内部共振中的脉动速度，系统中会引起参量激励。采用多尺度摄动技术直接法求解该问题。通过应用延拓算法提取各种稳定性和分叉现象等非线性特征。研究了平凡状态稳定性图以及粘性和材料阻尼的影响。脉动速度分量、内部频率失谐参数、轴向刚度、详细分析了振动响应的参数失谐参数。在铰链夹紧梁的研究中，解析-数值方法揭示了在联合参数和内部共振下丰富而有趣的非线性现象，这些现象在现有文献中是不可用的。