  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.
