Optimum parameters of tuned mass damper-inerter for damped structure under seismic excitation

• Published in: International journal of dynamics and control Vol. 10; no. 5; pp. 1322 - 1336
• Main Authors: Prakash, Shiv, Jangid, R. S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2022; Springer Nature B.V
• Subjects: Closed form solutions; Comparative studies; Complexity; Control; Control and Systems Theory; Curve fitting; Damping; Degrees of freedom; Dynamical Systems; Earthquake dampers; Earthquakes; Energy dissipation; Engineering; Exact solutions; Frame structures; Optimization; Parameters; Seismic response; Tuning; Vibration; Vibration isolators; Optimum parameters; Seismic excitation; Tuned mass damper inerter; Floor displacement; Closed-form expression; Stationary excitation; Floor accelerations
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-022-00911-x

The optimum tuning frequency ratio and damping of the tuned mass damper inerter (TMDI) used in damped single-degree-of-freedom (SDOF) structure subjected to stationary white-noise earthquake excitation is obtained with the help of numerical searching technique. Minimization of the mean-square absolute acceleration and relative displacement of the SDOF structure, as well as maximization of the energy dissipation index, are chosen as the criteria for optimal design. A curve-fitting method is used then to derive closed-form expressions for TMDI damping, tuning frequency, and optimized response which can easily be used for practical applications. The deviation of the optimal values obtained using proposed closed-form expressions is found to be negligible and therefore these expressions are convenient for the optimal effective design of TMDI for various structures. The usefulness of the proposed expressions of the TMDI parameters is then applied to multi-degree-of-freedom (MDOF) framed structures and a comparative study of the seismic response with and without TMDI (tuned for optimization of various objective functions) is done under real earthquake ground excitations. It is seen that an optimally designed TMDI is able to reduce the acceleration and displacement response of the MDOF structures.