关键词: 振动与波, 梁, 接触, 非线性振动, Runge-Kutta法, 分岔图, 混沌

Abstract: A piecewise linear dynamic model of the three-support elastic contact beam is established by considering the contact behavior between the elastic beam and the support spring. Use the assumed mode method to give the transverse displacement equation of the contact supporting beam, and the kinetic energy and potential energy of the supporting spring under the beam and contact state were derived. The vibration differential equation of the contact supporting beam was derived through the energy variation principle. The Runge-Kutta method was used to solve the beam's time and frequency domain response under harmonic excitation. The theoretical calculation results were in favorable agreement with those of the finite element method, which verifies the accuracy of the method. With the help of bifurcation diagram analysis, it is shown that different excitation amplitude, excitation frequency, and spring stiffness coefficient cause the contact supporting beam to have varying periodic or chaotic motions, which affect the nonlinear vibration characteristics of the contact supporting beams.