Optimum parameters of variant tuned mass damper using equal eigenvalue criterion

Abstract

AbstractIn this study, optimum parameters of a variant tuned mass damper (V‐TMD) wherein, damper is connected to the ground are obtained using equal eigenvalue (EEV) criterion. In EEV, TMD parameters are obtained by equating eigenvalues of two modes. By equating eigenvalues, the modal damping ratios (i.e., negative real part of the eigenvalue) become equal and maximum in two modes. This optimum condition is achieved by finding the roots of a sixth order polynomial. One of the novel findings is regarding the existence of two sets of optimum parameters, out of which, one set matches exactly with one of the earlier study. Regions in which, single and two sets of optimum parameters exist, are clearly brought out. Performance of V‐TMD is demonstrated for harmonic as well as earthquake excitation. It is noted that displacement as well as acceleration of the main system reduces due to V‐TMD. Another significant finding is that the real part of eigenvalues of V‐TMD is larger than that of classical tuned mass damper (C‐TMD), which leads to faster decay of earthquake response and lower peak response. The optimum parameters obtained in this study, pertain to linear SDOF and V‐TMD.