Modeling of laminated rubber bearings using an analytical stiffness matrix

In this paper from Haringx s theory, which considers lateral displacement and rotation angle in a rubber column as two independent variables, the mechanical behaviors of the column are analyzed. A 4 4 analytical stiffness matrix of the rubber column is obtained from a closed form solution, which is derived in the article. Then rigid body motion relations are used to transfer the stiffness matrix to another stiffness matrix that includes a rigid plate. Through the resulting stiffness matrix and linear theory, a stiffness summation procedure is used to construct an analysis model for a laminated rubber bearing. Because the present model represents one element constructed from a single rubber layer, a model of a complete bearing can be built up from a number of elements. The model overcomes many drawbacks of the original Haringx s theory, which treats the laminated rubber bearings as an equivalent continuous column. Comparisons of theoretical and experimental results show that the present analysis model has good accuracy for analyzing laminated rubber bearings. Examples are presented to demonstrate the validity of the developed method in predicting the horizontal stiffness and buckling load of laminated rubber bearings with different geometric parameters and boundary conditions.