# Model Order Reduction for Temperature-Dependent Nonlinear Mechanical Systems: A Multiple Scales Approach

## TL;DR

This paper introduces a multiple scales approach for model order reduction in temperature-dependent nonlinear mechanical systems, effectively capturing slow thermal dynamics and improving accuracy over traditional methods.

## Contribution

It develops an adaptive reduction basis that varies with temperature, providing a systematic way to reduce complex thermo-mechanical models.

## Key findings

- Achieves better accuracy than standard Galerkin projection.
- Reduces the number of unknowns in the models.
- Demonstrates effectiveness on linear and nonlinear beam examples.

## Abstract

The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduce the thermo-mechanical structural models with a slowly-varying temperature distribution in a systematic manner. In the process, we construct a reduction basis that adapts according to the instantaneous temperature distribution of the structure, facilitating an efficient reduction in the number of unknown. As a proof of concept, we demonstrate the method on a range of linear and nonlinear beam examples and obtain a consistently better accuracy and reduction in the number of unknowns than standard the Galerkin projection using a constant basis.