Nonlinear Model for Lead–Rubber Bearings Including Axial-Load Effects

Existing models for isolation bearings neglect certain aspects of their response behavior. For instance, rubber bearings have been observed to decrease in stiffness with increasing axial load, and soften in the vertical direction at large lateral deformations. The yield strength of lead–rubber bearings has also been observed to vary with axial load, such that a lightly loaded bearing may not achieve its theoretical strength. Models that include these axial-load effects in lead–rubber bearings are developed by extending an existing linear two-spring model to include nonlinear behavior. The nonlinearity includes an empirical equation for the experimentally observed variation of yield strength. For numerical implementation, the bearing forces are found by solving the nonlinear equilibrium and kinematic equations using Newton's method, and the instantaneous bearing stiffness matrix is formed from the differentials of these equations. The response behavior of the models is confirmed by comparison with experimental data.