Analysis of mechanical properties of laminated rubber bearings based on transfer matrix method

Abstract

Laminated rubber bearings are constructed from alternating layers of rubber vulcanized to reinforcing steel shims, therefore, they can be treated as periodic structures. The transfer matrix method (TMM) is developed to analyze mechanical behaviors of the periodic bearings subjected to a compressive axial load and a lateral shear deformation. The periodic model can account for the effect of thicknesses, material properties and boundary conditions of each rubber and steel layer, on the details of mechanical behaviors between interlaminated layers. Haringx’s theory for the individual rubber layer and rigid body motion theory for the steel shim are utilized in the development of the model. Hence, the proposed approach overcomes Haringx’s theoretical drawback, which assumes the entire laminated rubber bearings as an equivalent continuous column, and is also a robust alternative to the stiffness matrix method through a complex assembly of a number of identical periodic elements. Comparisons with Haringx’s results show that TMM has good accuracy for analyzing laminated rubber bearings. The introduction of the pattern of periodic structure along with TMM provides a viable means for determining mechanical properties of laminated rubber bearings with different configurations by only changing the number of periodic elements and thicknesses of the layers.