Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams
Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams
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DOI：
10.1016/j.ijsolstr.2008.08.002
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发表时间：
2008-12
影响因子：
3.6
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
考虑轴向运动的三次非线性粘弹性Rayleigh梁，通过几何关系、本构关系和动力学关系，推导出控制大振幅振动的运动偏微分方程组。将多尺度法直接应用于运动控制方程，并考虑可解条件，得到了系统的线性和非线性频率及振型的解析表达式。在阻尼项的存在下，可以看出系统的幅值是指数时变的，因此，系统的非线性固有频率将是时变的。对于共振情况，通过考虑可解性条件和劳斯-赫尔维茨判据，解析地给出了稳定性条件。最后，通过参数研究，研究了系统参数对系统振动行为、稳定性和分叉点的影响。
An axially moving visco-elastic Rayleigh beam with cubic non-linearity is considered, and the governing partial-differential equation of motion for large amplitude vibration is derived through geometrical, constitutive, and dynamical relations. By directly applying the method of multiple scales to the governing equations of motion, and considering the solvability condition, the linear and non-linear frequencies and mode shapes of the system are analytically formulated. In the presence of damping terms, it can be seen that the amplitude is exponentially time-dependent, and as a result, the non-linear natural frequencies of the system will be time-dependent. For the resonance case, through considering the solvability condition and Routh–Hurwitz criterion, the stability conditions are developed analytically. Eventually, the effects of system parameters on the vibrational behavior, stability and bifurcation points of the system are investigated through parametric studies.