Analytical mechanical model for laminated rubber bearings including crack effect

Abstract

The buckling phenomenon and deformation distribution of the laminated rubber bearing, taking into account the crack effect, are predicted by the period structure assumption and transfer matrix method (TMM). A concentrated flexural spring is utilized to simulate the local flexural stiffness deterioration that arises from the crack. The solutions of the individual rubber layer derived from Haringx’s column theory are formulated in the development of the crack model, and the inside steel shim is modeled as a rigid body whose transfer relation is then combined with that of the rubber layer. The resulting total transfer matrix, along with the boundary conditions, is applied to determine the horizontal stiffness and critical buckling load of the bearing with a single, or multiple cracks. Experimental data demonstrates the validity of the proposed analytical model. The results show that for a single crack, the least decrease in critical buckling load occurs when the crack is vertically centered along the height of the bearing; when the crack is closer to the top or bottom of the bearing, the critical buckling load may reduce by about half for a high level of deterioration. Two or multiple cracks make the critical buckling load decreased rapidly, especially for cracks in different rubber layers; nevertheless, not only the nearer these cracks approach the bearing center but also the much closer these cracks are together, the less the critical buckling load decreases.