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

TL;DR

This paper introduces a data-driven model order reduction technique for piecewise-linear nonlinear systems using dynamic mode decomposition, enabling efficient and accurate analysis of complex structural dynamics.

Contribution

It presents a novel DMD-based model reduction method tailored for piecewise-linear systems, incorporating impulse response snapshots and Galerkin projection for improved efficiency.

Findings

ROMs accurately predict forced responses

Method effectively handles contact nonlinearities

Reduced computational cost compared to full models

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 viewpoint. 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.