Study of an electromechanical nonlinear vibration absorber: Design via analytical approach

Abstract

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.

Tuning inter-modal energy exchanges of a nonlinear electromechanical beam by a nonlinear circuit

“…34 that electrical components affect the geometry of the SIM. This will lead to identify effects of these parameters on the behaviour of the electromechanical system [37]. There is a critical value of the inductance L 0 which divides the geometry of the SIM into monotone and non monotone [37].…”

“…This nonlinear behaviour was produced by the inherent nonlinearities of the electromechanical system. Then, we studied the possibility of using an adaptable nonlinear circuit when the system originally does not present any internal resonance [37]: It was shown that the components of the nonlinear circuit can be tuned to obtain desired dynamical behaviours of the system. This article is dealing with the use of an adaptable nonlinear circuit to master an inter-modal energy exchanges between two resonant modes of an electromechanical structure.…”

Detection of different dynamics of two coupled oscillators including a time-dependent cubic nonlinearity

“…These multi-physics systems can be used as sensors and actuators [6]. Their parameters can be changed with a low amount of energy, which give some adaptabilities to the such control systems [7,8,9,10,11].…”

Nonlinear Energy Sink and Targeted Energy Transfer in Smart Structures

“…More recently, in the field of smart structures and materials, piezoelectric vibration absorbers with nonlinear damping circuits gained popularity. It was first proposed already in 2009 [18] but has received more attention in the last few years, both theoretically and experimentally [19][20][21][22][23][24]. Here, a piezoelectric material is bonded to a primary system.…”