This study focuses on the modeling of tuned liquid dampers (TLDs) with triangular-bottom, sloped-bottom, parabolic-bottom, and flat-bottom tanks using the linear long wave theory. The energy dissipated by damping screens is modeled theoretically utilizing the method of virtual work. In this proposed model, only the fundamental sloshing mode is considered, and the assumption of small free surface fluid response amplitude is made. Subsequently, the equivalent mechanical properties including effective mass, natural frequency, and damping ratio of the TLDs, having different tank geometries, are compared. It is found that the normalized effective mass ratio values for a parabolic-bottom tank and a sloped-bottom tank with a sloping angle of 20 deg are larger than the normalized effective mass ratio values for triangular-bottom and flat-bottom tanks. An increase in the normalized effective mass ratio indicates that a greater portion of the water inside the tank participates in the sloshing motion. The derived equivalent mechanical models for the TLD tank geometries considered in this study can be used for the preliminary design of structural-TLD systems.

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