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基于振型转换的思想,提出了一种求解分段线性边界条件,以及可将其他非线性边界条件转化为分段线性边界条件的连续体振动问题的方法———相对振型转换法(Relative Mode Transfer Method,RMTM),用该法研究了端点带双阻挡悬臂梁的非线性振动。利用相对振型转换法处理了梁的接触振型与非接触振型的振动转换,与Moon于1983年所提方法进行了相互印证,通过时程图与幅频响应图,将两种方法得到的梁端点响应的结果进行对比,证实了相对振型转换法的正确性;并研究了一类边界条件梁的非线性振动,通过梁端点的幅值响应的分岔图,讨论了振型之间的耦合、模态阻尼及端点弹簧刚度对梁端点响应的影响。结果表明,弹簧刚度、阻尼、激励力等不同的参数组合可以导致梁的单周期运动、多周期运动以及混沌运动,得到了上述复杂非线性响应在激励力频域上存在的区域。
Based on the idea of modal transformation, a method to solve the piecewise linear boundary condition and the continuum vibration problem that can transform other non-linear boundary conditions into piecewise linear boundary conditions are proposed. Mode Transfer Method, RMTM) is used to study the nonlinear vibration of the end-point double-barrier cantilever beams. The relative vibration mode conversion method was used to deal with the vibration transformation of the contact and non-contact vibration modes of the beam, which was mutually confirmed by Moon’s method in 1983. Through the time-history and amplitude-frequency response diagrams, The results show that the relative shape conversion method is correct, and the nonlinear vibration of a kind of beam with boundary condition is studied. By means of the bifurcation diagram of the amplitude response of the beam end, Effect of Coupling, Modal Damping and End Spring Stiffness on Beam End Response. The results show that the spring stiffness, damping, excitation force and other different combinations of parameters can lead to the single-period motion, multi-period motion and chaotic motion of the beam, and the complex nonlinear response exists in the region of the excitation frequency.