Mathematical Modelling & Numerical Analysis of Passive Multimode Tuned Mass Damper Mechanism for a Multiple Degree of Freedom Structure

EasyChair Preprint 4661

Abstract

A single Tuned Mass Damper (TMD) can only suppress vibration of the assigned mode shape of a structure. For controlling multimode vibrations, Multiple Tuned Mass Damper (MTMD) is needed. In this study, mathematical modelling & numerical evaluation of the proposed MTMD as a vibration suppression mechanism is performed comprehensively by transforming structural model into an equivalent lumped mass-spring-dashpot system with consideration of Rayleigh damping hypotheses. The main structural model is designed as a linear time-invariant system and the equations of motions were derived using transfer function. The transfer function then further simplified in a state space representation to cater the analysis complexity. The time history & frequency response analysis of this study including the vibration control effect of attaching the various TMD arrangements to a three-story structure due to ground excitation input. A single TMD is first been designed to be tuned according to different mode shapes of uncontrolled primary structure. The influence of parameters such auxiliary mass ratio, optimum damping ratio, and optimum frequency ratio is identified numerically and the performance of structural control mechanism is analyzed for both single TMD and MTMD arrangement with additional base isolation system. The optimal placement of control devices is also justified using defined objective functions purposely to maximize system effectiveness and the robustness of the proposed mechanism in terms of the distribution of natural frequencies of seismic input. The result show that by the attachment of TMD at all floors with additional base isolation system is capable of reducing significant amount of top floor RMS displacement for a solid 94.5% for the first floor, 97.6% for the second floor, and 71.9% for the third floor.

Keyphrases: Base isolation, Tuned mass damper, frequency response, transfer function

@booklet{EasyChair:4661,
  author    = {Afham Zulhusmi Bin Ahmad and Aminudin Abu and Lee Kee Quen and Nor Azizi Othman and Faridah Che In},
  title     = {Mathematical Modelling & Numerical Analysis of Passive Multimode Tuned Mass Damper Mechanism for a Multiple Degree of Freedom Structure},
  howpublished = {EasyChair Preprint 4661},
  year      = {EasyChair, 2020}}