Effect of Support Conditions on the Vibration of Laminated Composite Beams

Abstract

Laminated glass plate or beam used in the building industry is an architectural unit of the building formed by two or more thin glass plates or beams bonded together by an interlayer PVB (polyvinyl butyral). The behavior of laminated glass beams is complicated because the different materials have different elastic modulus. Laminated glass is very thin and can easily undergo large displacements, therefore, the equilibrium equations governing their behavior should be based on large deflection theory. In the present study, the effect of boundary conditions on the vibration of a laminated glass unit is investigated by considering the cases of simply supported and fixed supported laminated glass beams. Glass units considered in this study have two thin glass beams and an interlayer PVB. A mathematical model for the dynamic behavior of a laminated glass beam is developed using variational principles. The assumptions of the classical beam theory are valid. Three coupled partial differential equations which express the dynamic behavior are obtained for lateral and axial displacements. By solving these equations, the effect of boundary conditions on the natural frequencies is observed in figures depicting displacement versus angular frequency.