Abstract
In this paper, we study a hysterically damped tuned mass system. We note that tuned mass dampers are extensively used in practical systems in order to reduce the dynamic response of the primary structures. The theory of tuned mass systems with viscous damping is well established. Simple tuned mass systems, with linear viscous damping, are analytically tractable. In reality, in many systems, we see damping are hysteretic in nature. Hysteresis is a strongly nonlinear phenomenon. Analytical study of tuned mass systems with hysteretic damping is therefore challenging. Here, we use a rate-independent hysteresis model developed by Biswas et al. in Int J Mech Sci 108:61–71, 2016, as the damper. We use numerical and semi-analytical approaches to study the dynamic responses of systems. The amplitude versus frequency curves shows two resonance peaks. The numerical and analytical results show good match.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Frahm H (1909) Device for damping vibrations of bodies. US Patent No 989, 958
Ormondroyd J, Den Hartog JP (1928) The theory of the dynamic vibration absorber. ASME J Appl Mech 50:9–22
Den Hartog JP (1947) Mechanical vibration. McGraw–Hill, New York
Jangid RS, Datta TK (1995) Seismic behavior of the base-isolated buildings: a state-of-the art review. Struct Build 110(2):186–203
Soto MG, Adeli H (2013) Tuned mass dampers. Arch Comput Meth Eng 20:419–431
Elias S, Matsagar V (2017) Research developments in vibration control of structures using passive tuned mass dampers. Annu Rev Control 44:129–156
Randall SE, Halsted DM, Taylor DL (1981) Optimum vibration absorbers for linear damped systems. J Mech Des (ASME) 103:908–913
Starovetsky Y, Gendelman OV (2009) Vibration absorption in systems with a nonlinear energy sink: nonlinear damping. J Sound Vib 324(3–5):916–939
Gerges RR, Vickery BJ (2005) Design of tuned mass dampers incorporating wire rope springs: part I: dynamic representation of wire rope springs. Eng Struct 27:653–661
Gerges RR, Vickery BJ (2005) Design of tuned mass dampers incorporating wire rope springs: part II: simple design method. Eng Struct 27:662–674
Carpineto N, Lacarbonara W, Vestroni F (2014) Hysteretic tuned mass dampers for structural vibration mitigation. J Sound Vib 333:1302–1318
Lacarbonara W, Vestroni F (2002) Feasibility of a vibration absorber based on hysteresis. In: Proceedings of the Third World Congress on Structural Control, Como, Italy
Bouc R (1967) Forced vibration of mechanical systems with hysteresis. In: Proceedings of the 4th Conference on Nonlinear Oscillation, p 315, Prague
Wen Y (1976) Method for random vibration of hysteretic systems. J Eng Mech Div 102(2):249–263
Biswas S, Jana P, Chatterjee A (2016) Hysteretic damping in an elastic body with frictional microcracks. Int J Mech Sci 108:61–71
Balija S, Biswas S, Chatterjee A (2018) Stability aspects of the Hayes delay differential equation with scalable hysteresis. Nonlinear Dyn 93(3):1377–1393
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Rathore, K.K., Biswas, S. (2023). Multi-frequency Approximation for a Hysteretically Damped Tuned Mass System. In: Maurya, A., Srivastava, A.K., Jha, P.K., Pandey, S.M. (eds) Recent Trends in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-7709-1_10
Download citation
DOI: https://doi.org/10.1007/978-981-19-7709-1_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-7708-4
Online ISBN: 978-981-19-7709-1
eBook Packages: EngineeringEngineering (R0)