Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams
Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams
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DOI：
10.1016/j.apm.2009.12.019
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发表时间：
2010-10
影响因子：
5
通讯作者：
M. Ghayesh;Sara Balar
中科院分区：
文献类型：
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作者：
M. Ghayesh;Sara Balar
考虑了轴向运动Timoshenko梁的非线性参数振动和稳定性。第一个，只考虑横向位移第二个，同时考虑纵向和横向位移。采用能量法推导了两种模型的非线性偏微分方程组。将多尺度法直接应用于两种模型，利用一阶方程得到了振型方程和固有频率。然后，对阶方程考虑了共振情况下的可解性条件，并利用Routh-Hurwitz判据解析地给出了稳定性边界。最后，通过数值算例说明了上述非线性模型在行为上的差异。
Non-linear parametric vibration and stability of an axially moving Timoshenko beam are considered for two dynamic models; the first one, with considering only the transverse displacement and the second one, with considering both longitudinal and transverse displacements. The set of non-linear partial-differential equations of both models are derived using an energy approach. The method of multiple scales is applied directly to both models, and using the equation order one, the mode shape equations and natural frequencies are obtained. Then, for the equation order epsilon, the solvability conditions are considered for the resonance case and the stability boundaries are formulated analytically via Routh–Hurwitz criterion. Eventually, some numerical examples are provided to show the differences in the behavior of the above-mentioned non-linear models.