A non-linear model for elastic hysteresis in the time domain: Computational procedure
Dwaikat M.M.S. Spitas C. Spitas V.
October 2021SAGE Publications Ltd
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
2021#235Issue 204625 - 4636 pp.
Hysteretic damping of a material or structure loaded within its elastic region is the dissipation of mechanical energy at a rate independent of the frequency of vibration while at the same time directly proportional to the square of the displacement. Generally, reproducing this frequency-independent damping can be computationally complex and requires prior knowledge of the system’s natural frequencies or the full time history of the system’s response. In this paper, a new model and numerical procedure are proposed whereby hysteretic material damping is achieved in the time domain. The proposed procedure is developed based on modifying the viscous model through a correction factor calculated exclusively using the local response. The superiority of the proposed approach lies in its ability to capture material hysteresis without any knowledge of the eigen- or modal frequencies of the system and without knowledge of the past time history of the system’s response or the characteristics of any excitation forces. A numerical procedure is also presented for implementing the proposed model in vibration analysis. The simplicity of the approach enables its generalisation to continuous systems and to systems of multi-degrees of freedom as demonstrated herein. The proposed model is presented as a correction to the viscous damping model which makes it attractive to implement into commercial finite element package using user-defined element subroutines as demonstrated in this study.
finite element analysis , frequency-independent damping , Hysteresis , mechanical vibration , time-domain , viscous
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Department of Civil Engineering, An-Najah National University, Nablus, Palestine
Department of Mechanical and Aerospace Engineering, Nazarbayev University, Astana, Kazakhstan
School of Mechanical Engineering, National Technical University of Athens, Athens, Greece
Department of Civil Engineering
Department of Mechanical and Aerospace Engineering
School of Mechanical Engineering
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