The optimum inertial amplifier tuned mass dampers for nonlinear dynamic systems

Chowdhury, S., Banerjee, A. and Adhikari, S. (2023) The optimum inertial amplifier tuned mass dampers for nonlinear dynamic systems. International Journal of Applied Mechanics, 15(2), 2350009. (doi: 10.1142/s1758825123500096)

Abstract

The optimum inertial amplifier tuned mass dampers (IATMD) for vibration reduction of linear and nonlinear dynamic systems are introduced in this paper. H2 and H∞ optimization methods are applied to derive the exact closed-form expressions for optimal design parameters such as frequency and viscous damping ratios in simplified form mathematically for IATMD. From the parametric study, using these optimal closed-form solutions, a higher damper mass ratio, a higher amplifier mass ratio, and a lower inertial angle are recommended to design optimum IATMD to achieve robust dynamic response reduction capacity having moderate viscous damping and lower frequency ratios at an affordable range. The optimum IATMD systems are installed on top of linear and nonlinear single-degree-of-freedom systems to mitigate their dynamic responses of them. The linear dynamic responses are determined through transfer matrix formations, and nonlinear dynamic responses are derived using the harmonic balance (HB) method. H2 optimized IATMD is significantly 44.78 and 48.62 superior to the H2 optimized conventional tuned mass damper one (CTMD1) and conventional tuned mass damper two (CTMD2). Furthermore, H∞ optimized IATMD is significantly 39.98 superior to the H∞ optimized conventional tuned mass damper (CTMD). According to the nonlinear dynamic analysis, H2 optimized IATMD systems are significantly 35.33 , 76.97 , and 35.33 superior to the H2 optimized CTMD. Furthermore, H∞ optimized IATMD systems are significantly 25.92 , 73.64 , and 25.92 superior to the H∞ optimized CTMD. The results of this study are mathematically accurate and feasible for practical applications.

• Item Type: Articles
• Additional Information: The authors’ would like to acknowledge the Inspire faculty grant, Grant No. DST/ INSPIRE/04/2018/000052 for partial financial support for the project. SC would like to acknowledge the MHRD grant received from IIT Delhi during the period of this research work.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Adhikari, Professor Sondipon
• Authors: Chowdhury, S., Banerjee, A., and Adhikari, S.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal of Applied Mechanics
• Publisher: World Scientific Publishing
• ISSN: 1758-8251
• ISSN (Online): 1758-826X
• Published Online: 19 January 2023
• Copyright Holders: Copyright © World Scientific Publishing Europe Ltd.
• First Published: First published in International Journal of Applied Mechanics 15(2):2350009
• Publisher Policy: Reproduced in accordance with the publisher copyright policy