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Demonstrating the power of extended Masing models for hysteresis through model equivalencies and numerical investigation

Beck, James L. and Pei, Jin-Song (2022) Demonstrating the power of extended Masing models for hysteresis through model equivalencies and numerical investigation. Nonlinear Dynamics, 108 (2). pp. 827-856. ISSN 0924-090X. doi:10.1007/s11071-022-07237-5. https://resolver.caltech.edu/CaltechAUTHORS:20220310-207343000

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Abstract

The extended Masing model (EMM) is a powerful model for hysteresis that is theoretically sound, physically meaningful and computationally efficient. Any such model is defined by specifying a virgin loading curve and is implemented for arbitrary loadings using three simple hysteresis rules. A brief history of the development of these three switching rules is given. They can be accurately and efficiently implemented using a hybrid dynamical system approach where a state event algorithm is seamlessly combined with a time-stepping algorithm for numerical solution of the equations of motion when an EMM is used for the combined restoring and damping force. It is shown why each EMM is equivalent to an Iwan distributed-element model (DEM), which generalizes a multi-linear hysteresis system (a.k.a. Maxwell slip model) that consists of a finite number of elasto-plastic elements in parallel to an infinite number of such elements (countably many or a continuum of them). This model equivalency provides a physical basis for the choice of the three EMM rules. It is also noted that each EMM is also a classical Preisach model, a class of models that is well known in the mathematical literature on hysteresis. The extended Masing model is inherently for softening hysteresis but we show that a simple modification can be used to extend it to hardening hysteresis. It is noted that the EMM can also be extended to model deteriorating hysteresis. The hysteresis behavior of the EMM is further illustrated with examples of single-degree-of-freedom and two-degrees-of-freedom systems under dynamic excitation that use for the restoring force a specific EMM model whose defining virgin loading curve has a quite general parameterized form. It is shown that if the EMM model for the restoring force in a SDOF system that is subjected to earthquake excitation is replaced by a Bouc–Wen model with the same virgin loading curve, the hysteretic response changes dramatically and exhibits substantial drifting of the hysteresis loops. This behavior of the Bouc–Wen model is the result of a physical deficiency that was first noted four decades ago.


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https://doi.org/10.1007/s11071-022-07237-5DOIArticle
https://rdcu.be/cIIaDPublisherFree ReadCube access
https://doi.org/10.1007/s11071-022-07446-yDOICorrection
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ORCID:
AuthorORCID
Pei, Jin-Song0000-0002-1042-1859
Additional Information:© The Author(s), under exclusive licence to Springer Nature B.V. 2022. Received: 28 May 2020 / Accepted: 15 January 2022. The literature review and content in the appendix were initiated during the second author’s second sabbatical leave at the California Institute of Technology whose hospitality is appreciated. The partial support of the second author’s internal grant FIP 2018 from the University of Oklahoma during this leave is acknowledged. The main text was initiated during the second author’s teaching release in the fall of 2019. Professor Maarten Schoukens at TU/e, the Netherlands is acknowledged for her better understanding of multi-linear hysteresis systems (Maxwell-slip models), while Professor Johan Schoukens is acknowledged for introducing her to the Leuven model. At Columbia University, Professor Raimondo Betti is acknowledged for his hospitality. The pioneering vision of Professor Joseph Wright for applying the state event location algorithm to benefit nonlinear hysteresis modeling is acknowledged. Data availability. Data sharing not applicable to this article as no datasets were generated or analysed during the current study. The authors declare that they have no conflict of interest.
Errata:Beck, J.L., Pei, JS. Correction to: Demonstrating the power of extended Masing models for hysteresis through model equivalencies and numerical investigation. Nonlinear Dyn (2022). https://doi.org/10.1007/s11071-022-07446-y
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Funding AgencyGrant Number
University of OklahomaUNSPECIFIED
Issue or Number:2
DOI:10.1007/s11071-022-07237-5
Record Number:CaltechAUTHORS:20220310-207343000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220310-207343000
Official Citation:Beck, J.L., Pei, JS. Demonstrating the power of extended Masing models for hysteresis through model equivalencies and numerical investigation. Nonlinear Dyn 108, 827–856 (2022). https://doi.org/10.1007/s11071-022-07237-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113871
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:11 Mar 2022 20:58
Last Modified:26 Apr 2022 20:17

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