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Data-driven model order reduction for structures with piecewise linear nonlinearity using dynamic mode decomposition

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Abstract

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoints. In this paper, a data-driven model order reduction method for piecewise-linear systems is proposed, which is based on dynamic mode decomposition (DMD). The overview of the concept of DMD is provided, and its application to model order reduction for nonlinear systems based on Galerkin projection is explained. The proposed approach uses impulse responses of the system to obtain snapshots of the state variables. The snapshots are then used to extract the dynamic modes that are used to form the projection basis vectors. The dynamics described by the equations of motion of the original full-order system are then projected onto the subspace spanned by the basis vectors. This produces a system with much smaller number of degrees of freedom (DOFs). The proposed method is applied to two representative examples of piecewise linear systems: a cantilevered beam subjected to an elastic stop at its end, and a bonded plates assembly with partial debonding. The reduced order models (ROMs) of these systems are constructed by using the Galerkin projection of the equation of motion with DMD modes alone, or DMD modes with a set of classical constraint modes to be able to handle the contact nonlinearity efficiently. The obtained ROMs are used for the nonlinear forced response analysis of the systems under harmonic loading. It is shown that the ROMs constructed by the proposed method produce accurate forced response results.

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Data availability

The dataset generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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Funding

This project was supported in part by Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research(C), grant number JP20K11855.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Meiji University, Kawasaki, Kanagawa, 214-8571, Japan

    Akira Saito

  2. Toyota Research Institute of North America, Toyota Motor North America, Inc., Ann Arbor, MI, 48105, USA

    Masato Tanaka

Authors
  1. Akira Saito
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  2. Masato Tanaka
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Contributions

Both authors contributed to the study conception, design and analysis. Simulations were implemented and performed mainly by A. Saito. The first draft of the manuscript was written by A. Saito and M. Tanaka commented on the draft of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Akira Saito.

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Saito, A., Tanaka, M. Data-driven model order reduction for structures with piecewise linear nonlinearity using dynamic mode decomposition. Nonlinear Dyn 111, 20597–20616 (2023). https://doi.org/10.1007/s11071-023-08958-x

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