Study on Analytical Model of Nonlinear Vibration for Elastic Plates With Gaps Under Random Waves

Abstract

In this paper, an analytical model for the nonlinear elastic-plastic vibration for long plates with gaps subjected to random vibrations is considered. The nonlinear vibration is caused by the collision phenomena between a mass through a gap and plates with thickness of 0.5, 0.6, and 0.8 mm. An elastic perfectly plastic solid material is assumed in some cases, which adds another aspect to the nonlinear behavior of the system. The material characteristic of the steel is assumed to be an elasto-plasticity solid model. A restoring force characteristic is obtained as the nonlinear vibration of a cubic equation for 0.5, 0.6, and 0.8 mm, the thickness of the plates by experiments. Now the analytical model is proposed by the elasto-plasticity solid model. The relation between the displacement and the force is described by a complicated equation. The curve from the analytical model is called a deflection curve. The results by the analytical model are compared with the results by the experimental model. The restoring force characteristics by the analysis agree with those of the experiment. The restoring force characteristics of the analysis are described using cubic equations. The simple analysis model for evaluation of the vibration characteristic of the nonlinear vibration system, which performs collision vibration with gaps, is proposed by elasto-plasticity solid model in this paper. The results of this proposed analytical model agree with the experimental results better than the results of the minimum of error of square.