Subharmonic resonance of a clamped-clamped buckled beam with 1∶1 internal resonance under base harmonic excitations

• 作者: Jianliang HUANG Junda LI
• 来源期刊: 应用数学和力学（英文版）
• 学科: 物理学
• 年，卷（期）: 2020,（12）
• 页码范围: 1881-1896
• 页数: 16页
• 分类号: O322
• 语种: 英文

摘要

The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated.The nonlinear partial integrodifferential equation of the motion of the buckled beam with both quadratic and cubic nonlinearities is given by using Hamilton's principle.A set of second-order nonlinear ordinary differential equations are obtained by spatial discretization with the Galerkin method.A high-dimensional model of the buckled beam is derived,concerning nonlinear coupling.The incremental harmonic balance (IHB) method is used to achieve the periodic solutions of the high-dimensional model of the buckled beam to observe the nonlinear frequency response curve and the nonlinear amplitude response curve,and the Floquet theory is used to analyze the stability of the periodic solutions.Attention is focused on the subharmonic resonance caused by the internal resonance as the excitation frequency near twice of the first natural frequency of the buckled beam with/without the antisymmetric modes being excited.Bifurcations including the saddle-node,Hopf,perioddoubling,and symmetry-breaking bifurcations are observed.Furthermore,quasi-periodic motion is observed by using the fourth-order Runge-Kutta method,which results from the Hopf bifurcation of the response of the buckled beam with the anti-symmetric modes being excited.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	Junda LI		1	0	0.0	0.0
2	Jianliang HUANG		1	0	0.0	0.0