Frequency analysis and control of sloshing coupled by elastic walls and foundation with smoothed particle hydrodynamics method

Abstract

Broadband stochastic excitations from environment such as seismic activities, sea waves, wind gusts, and tremors can lead to the terrible damages of tall structures and buildings which usually have a low amount of vibration damping. Tuned liquid dampers (TLD) have been considered for around thirty years regarding their ability for passive suppression and absorb the vibration energy in such structures. In this paper, the fluid-structure interaction of a two-dimensional rectangular tank with elastic side walls and foundation is investigated by the smoothed particle hydrodynamics (SPH) method. First, the implementation of SPH for the frequency analysis of a rectangular container with flexible boundaries, partially filled with liquid, is described. The governing equations of the sloshing of an inviscid liquid in a two-dimensional Cartesian coordinate system coupled with the thin plate vibration on sides are linearized and solved by the SPH method. The sloshing and bulging modes of the system are derived and discussed in this paper. The results of the frequency spectrum of the sloshing tank coupled with the spring-damper system are analyzed and compared with the mechanical equivalent system. Results are validated by analytical benchmark and show the applicability as well as the simplicity of the SPH method for analytical vibration analysis of a fluid-structure coupled system. Then various control method including: Active mass damping (AMD) control designed based on proportional feedback control, the tuned liquid damper (TLD) control based on the analytical model, and a hybrid method of active tuned liquid damper (ATLD) are modeled and compared in a one-story structure. Results demonstrated that although the AMD is more efficient and stable in a specific range of feedback coefficient, the proposed ATLD is reliable in a wider range of control parameters.