【摘要】 为进一步完善弹性地基上梁的非线性振动理论以及满足实际工程的需要,本文对三种联合共振情况进行了研究。文中基于已建立的Winkler地基上有限长梁的非线性振动方程,运用Galerkin离散法以及多尺度法推导其稳态运动方程组,分析了主/次联合共振时,结构参数及初始条件对系统幅频响应曲线、调谐-相位曲线的影响,初步探讨了主/超联合共振、次/超联合共振的基本性质。研究结果表明:当且仅当两个激励频率是可公度关系时,联合共振才存在稳态响应;对于一个给定的调谐参数,系统最多存在七个解,而解的最终形式是由初始条件决定;系统参数及初始条件的微小变动,可能会激烈地改变系统的响应;工程中为了较好地抑制结构的振动,必须选择合适的方法提高系统的刚度。更多还原

【Abstract】 In order to improve the nonlinear vibration theory for the finite-length beams on the elastic foundation and satisfy the requirements of practical engineering,this paper aims to study the primary,sub-harmonic and super-harmonic excitations occure simultaneously.Based on the derived nonlinear vibration equations of finite-length beams on the Winkler foundation,the method of Galerkin and multiple scales are adopted to formulate the equations of steady-state motions.We consider a case of double resonance in which primary and sub-harmonic resonances exist simultaneously and analyze the effect of the system parameters and the initial conditions on the amplitude-frequency response curves and the phase-tuning curves.Numerical results are presented that the steady state response is periodic,when two resonances occur simutaneously and the excitation frequencies are commensurable.There are as many as seven solutions for a given tuning parameter,in case of more than one stable solution,whose final forms will be determined by their initial conditions.It is also found that small changes in the system parameters or the initial conditions might drastically change the response of the system.To control the resonances of the beam in engineering,an appropriate way is demanded to enhance the stiffness of the system.更多还原