Multi-frequency Approximation for a Hysteretically Damped Tuned Mass System

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. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.