轴向运动粘弹性Rayleigh梁的参激振动稳定性
发布时间：2018-09-14 09:42
【摘要】：研究了轴向运动粘弹性Rayleigh梁参激振动的稳定性。根据广义哈密顿原理建立轴向运动Rayleigh梁横向振动的控制方程,同时考虑轴力的变化。采用多尺度方法直接求解控制方程,推导出主共振和组合共振的可解性条件;利用Routh-Hurwitz稳定性判据导出了稳定性边界方程;进而确定梁两端简支和固支边界条件下,因共振而产生的失稳区域。数值算例给出了两端简支和固支边界条件下弯曲刚度,支撑刚度,粘弹性系数以及平均速度对前两阶主共振及组合共振稳定性区域的影响。
[Abstract]:The stability of parametric vibration of viscoelastic Rayleigh beams with axial motion is studied. Based on the generalized Hamiltonian principle, the governing equations of lateral vibration of axially moving Rayleigh beams are established, and the variation of axial forces is considered. The solvability conditions of main resonance and combined resonance are derived by using multi-scale method, the stability boundary equation is derived by using Routh-Hurwitz stability criterion, and the boundary conditions of simple support and fixed support at both ends of beam are determined. A region of instability resulting from resonance. Numerical examples show the effects of bending stiffness, bracing stiffness, viscoelastic coefficient and average velocity on the first two order principal resonance and combined resonance stability region under the boundary conditions of simple support and fixed support.
【作者单位】： 上海应用技术大学;广州明珞汽车装备有限公司;
【基金】：国家自然科学基金项目(11202136)
【分类号】：TB535
[Abstract]:The stability of parametric vibration of viscoelastic Rayleigh beams with axial motion is studied. Based on the generalized Hamiltonian principle, the governing equations of lateral vibration of axially moving Rayleigh beams are established, and the variation of axial forces is considered. The solvability conditions of main resonance and combined resonance are derived by using multi-scale method, the stability boundary equation is derived by using Routh-Hurwitz stability criterion, and the boundary conditions of simple support and fixed support at both ends of beam are determined. A region of instability resulting from resonance. Numerical examples show the effects of bending stiffness, bracing stiffness, viscoelastic coefficient and average velocity on the first two order principal resonance and combined resonance stability region under the boundary conditions of simple support and fixed support.
【作者单位】： 上海应用技术大学;广州明珞汽车装备有限公司;
【基金】：国家自然科学基金项目(11202136)
【分类号】：TB535
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