Study of an electromechanical nonlinear vibration absorber: Design via analytical approach
Résumé
This article deals with the behavior and design of a homogeneous beam linked to an electrical absorber, via a piezoelectric
material patched on the beam. The beam presents a cubic nonlinearity, which is consistent with geometrical nonlinearities
for clamped-free beams. A cubic nonlinearity is added to the electrical circuit for similarity purposes. The
coupled electromechanical equations are reduced to a two degrees of freedom system. The equation representing the
mechanical response of the system is seen as the main system, whereas the equation coming from the electrical circuit
would represent a nonlinear absorber. An analytical treatment at different time scales is endowed to identify electrical
coefficients allowing the design of the electromechanical vibration absorber behavior. The equilibrium and singular points
are identified, allowing the definition of ranges of forcing amplitudes leading to periodic and modulated regimes. The analytical
results are compared with those obtained from direct numerical integration of the two degree of freedom
system.