A non-linear model for elastic hysteresis in the time domain: Computational procedure

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...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2021-10, Vol.235 (20), p.4625-4636
Main Authors: Dwaikat, MMS, Spitas, C, Spitas, V
Format: Article
Language:English
Subjects:
Hysteresis
Mathematical analysis
Mathematical models
Resonant frequencies
Time domain analysis
Vibration analysis
Viscous damping
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Summary: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.
ISSN:0954-4062
2041-2983
DOI:10.1177/0954406220982020