On non-linear dynamics of a coupled electro-mechanical system

Electro-mechanical devices are an example
of coupled multi-disciplinary weakly non-linear systems.
Dynamics of such systems is described in this
paper by means of two mutually coupled differential
equations. The first one, describing an electrical
system, is of the first order and the second one, for
mechanical system, is of the second order. The governing
equations are coupled via linear and weakly
non-linear terms. A classical perturbation method, a
method of multiple scales, is used to find a steadystate
response of the electro-mechanical system exposed
to a harmonic close-resonance mechanical excitation.
The results are verified using a numerical model
created in MATLAB Simulink environment. Effect of
non-linear terms on dynamical response of the coupled
system is investigated; the backbone and envelope
curves are analyzed. The two phenomena, which
exist in the electro-mechanical system: (a) detuning
(i.e. a natural frequency variation) and (b) damping
(i.e. a decay in the amplitude of vibration), are analyzed
further. An applicability range of the mathematical
model is assessed.