基础谐波激励单侧约束简支梁系统的动力学特征分析 1)

为研究间隙碰撞对系统动力学响应的影响,以理想简支梁的振型函数为Rayleigh--Ritz基函数建立了单侧约束简支梁系统的非线性离散动力学方程组,应用数值方法研究了系统在基础谐波激励下的动力学响应特征及其对共振频率线性等效方法适用性的影响。研究表明：非线性动力学系统间隙产生的局部碰撞,使得系统振动能量在系统各阶模态之间转移,使得线性等效方法失效;即使进行非线性分析,也需要考虑系统固有频率远大于激励频段上限的模态。

DYNAMICAL CHARACTERISTICS ANALYSIS FOR UNILATERAL CONSTRAINED SIMPLY SUPPORTED BEAM WITH HARMONIC WAVE EXCITATION1)

In order to study the influence of the gap collision on the dynamic response of the system, the nonlinear discrete dynamics equations of the unilateral constrained simply supported beam system are derived by using the Rayleigh-Ritz function as the mode function of an ideal simply supported beam. The dynamic response characteristics of the system under the fundamental harmonic excitation and its influence on the applicability of the linear equivalent method of the resonant frequency are studied by numerical methods. It is shown that the local collision caused by the gap of the nonlinear dynamic system will lead to the system vibration energy transfer between the various modes of the system, which makes the linear equivalent method invalid. Even in nonlinear analysis, it is necessary to consider the modes in which the natural frequency of the system is much larger than the upper limit of the excitation band.