Gaussian closure technique for a simple tank model with non-zero mean random load and elasto-plasticity

Abstract

Previously, it was shown how the behavior of chain-like structures including hysteretic elements as described by the Bouc model under white noise excitation can be calculated using Gaussian closure. The method results in analytic expressions for the temporal evolution of the statistical moments. Using the example of a liquid-filled tank, the Gaussian closure is generalized to the case of a filtered white noise with a slowly varying intensity as may occur during earthquakes. The complexity of the model is further enhanced for a case that lacks an elastic restoring force at the hysteretic node that couples the tank model with the surface. The new tank model comprises three mechanical degrees of freedom. The first degree of freedom is the movement of mass of the tank. The second degree of freedom is the movement of the swapping mass of the fluid in the tank. The third degree of freedom is the movement of the impulsive mass that is coupled more stiffly.