Nonlinear dynamics analysis of a membrane Stirling engine: Starting and stable operation

TL;DR

This paper models and analyzes the nonlinear dynamics of a miniaturized membrane Stirling engine, focusing on startup and stable operation, using stability analysis and normal form theory to predict limit cycles and optimize design.

Contribution

It introduces a semi-analytical model incorporating nonlinear effects and uses stability analysis to predict engine startup and steady-state behavior, aiding design optimization.

Findings

Predicts engine startup conditions.

Identifies instability leading to steady state.

Simplifies system equations without losing dynamics.

Abstract

This paper presents the work devoted to the study of the operation of a miniaturized membrane Stirling engine. Indeed, such an engine relies on the dynamic coupling of the motion of two membranes to achieve a prime mover Stirling thermodynamic cycle. The modelling of the system introduces the large vibration amplitudes of the membrane as well as the nonlinear dissipative effects associated to the fluid flow within the engine. The nonlinearities are expressed as polynomial functions with quadratic and cubic terms. This paper displays the stability analysis to predict the starting of the engine and the instability problem which leads to the steady state behaviour. The centre manifold - normal form theory is used to obtain the simplest expression for the limit cycle amplitudes. The approach allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The model intends to be used as a semi analytical design tool for the optimization of miniaturized Stirling machines from the starting to the steady operation.