Optimal Step-by-Step Tuning Method for Variable Stiffness Semiactive Tuned Mass Dampers

A new method, optimal step-by-step tuning (OSST), is presented for the frequency adjustment of variable stiffness semiactive tuned mass dampers (SATMDs). In this method, the external excitation of the system fitted with a SATMD is divided into several time steps, and the response components are expressed as polynomial functions of the SATMD's stiffness. An objective function is defined, the minimization of which leads to the desired SATMD's stiffness in each time step. In order to assess the efficiency of the OSST method, a single-degree-of-freedom (SDOF) system equipped with an innovative SATMD under transient vibrations is considered. The system's response is obtained and compared with the following cases: (1) unity tuning ratio (UTR) method, in which the frequency of the SATMD is equal to the excitation frequency, and (2) constant tuning ratio (CTR) method, in which the ratio of the SATMD frequency to excitation frequency is a constant value close to unity. The results reveal the superiority of the OSST method in transient response reduction in comparison with the UTR and CTR methods.