Closed form optimal solution of a tuned liquid column damper for suppressing harmonic vibration of structures

Building vibration has become one of the major concerns to structural engineers. Being a vibration absorber, a tuned liquid column damper (TLCD) not only suppresses building vibration, but also acts as the water storage facility of a building. In view of this, the application of such damper is particularly suited for building structures. However, due to inherent nonlinear liquid damping, it is no doubt that a great deal of computational effort is required to search the optimum parameters of TLCD numerically. Therefore, this paper aims to develop a closed form solution scheme of TLCD-structure systems and the optimum parameters of TLCD that lead to the maximum vibration reduction of building structure, so as to facilitate the design of dampers. The developed closed form solution of TLCD-structure system is verified by comparing results obtained from the conventional iterative method. After having a satisfactory verification, the existence of the invariant points of a TLCD-structure system for the case of undamped primary structure is demonstrated. Explicit design formulas of TLCD for the case of undamped primary structures are obtained by optimizing the response at the two invariant points. The optimum parameters of TLCD for the case of damped primary structures are also investigated numerically. An approach for determining the optimum head loss coefficient of TLCD is proposed. Finally, an example is given to illustrate the design procedures of TLCD for suppressing harmonic type vibrations