Stochastic response of structures with fluid-containing appendages

Abstract

The influence of fluid-containing appendages on the dynamic response of multi-degree-of-freedom systems subjected to stochastic environmental loads, e.g., earthquakes, waves, or winds, is investigated. The modal properties of a system comprising of a fluid-containing appendage attached to a multi-degree-of-freedom system are expressed in terms of the individual dynamic properties of the primary and secondary systems. The primary system is modeled as a lumped mass multi-degree-of-freedom system. An equivalent lumped mass model of the sloshing fluid is used to represent the secondary system. All the frequencies of the secondary system that are less than or equal to the fundamental natural frequency of the primary system are included in the dynamic analysis of the combined system. The input to the system may be a stationary or a non-stationary white or filtered white noise vector-valued excitation. In this study the structural response to an earthquake represented by a non-stationary filtered white noise is computed at any time interval by utilizing the modal impulse-response function and approximating the envelope intensity function with a staircase unit impulse function. The formulation presented here renders the computational procedure very efficient by reducing the multiplicity of the integrals. The covariance matrices of the response components of the combined system are computed by using this formulation. The peak response values at any level on the structure may be obtained by following the evolutionary distribution of the extreme values. An important feature of the combined system is that the response of the primary system is suppressed when one of the sloshing modes of the secondary fluid appendage is tuned to the fundamental mode of the primary system. A building with a water tank situated at any floor, excited by an earthquake, is used to illustrate the methodology.