Vibration Analysis of a Partially Connected Double-Beam System with the Transfer Matrix Method and Identification of the Slap Phenomenon in the System

Abstract

This study concerns dynamic behavior of a partially connected double-beam system. This beam system is composed of two single beams and these beams are connected to each other by the distributed stiffness of which are located at certain regions. The governing equation of this double-beam system is composed of two fourth-order differential equations for each single beam. These two governing equations are coupled to each other by the partially distributed stiffness. And the coupling in the governing equations makes it difficult to analyze the dynamic behavior of this system. In this study, therefore, the difficulty has been overcome by using one assumption and one concept. The assumption is that the double beam is composed of two equivalent single beams. And the concept is concerned with the relative displacement between the two layers. In addition, the transfer matrix method is used to take problems concerned with discontinuity into account, which are generated by the distributed stiffness. And it is predicted that there will be the slap phenomenon in the double-beam system when the amplitude of the relative displacement is larger than the natural gap distance between the two layers. This phenomenon has been identified in experimental measurements.