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.