Theoretical and experimental study of piezoelectric nonlinear resonators for energy harvesting and vibrations control
Résumé
The aim of the work is to control the vibrations or to harvest some vibratory energy from a nonlinear
structure through modal energy exchanges of the system. To exchange energy within modes, internal
resonances between them are created [1]. We then intend to design the exchange of energy, thanks to
the nonlinear terms of the structure, to: (i) perform balance of modal energies, (ii) transfer energy of
“dangerous” modes to other one’s, (iii) transfer energy to particular modes to harvest it.
A structure composed of a cantilever homogeneous beam patched with one or two piezoelectric
materials, at certain positions on the beam, is studied. Two configurations are studied: the first one
with a piezoelectric patch on one side on top of the elastic beam, and the second one with two
collocated patches. Those two configurations have different effects on the nonlinear terms, because
of the axial symmetry or asymmetry it creates. We write the governing nonlinear equations of the
system, supposing an Euler Bernoulli beam with large deformations. The nonlinearities of the model
come from the large rotation nonlinearity of the beam [2] and the assumption of a nonlinear material
behaviour of the piezoelectric patches [3].
The positions of the piezoelectric patches are used to create the intended internal resonance. Written
in a general manner, the n th and the m th frequencies (ω n and ω m , respectively) are in internal
resonance if ω n ≈p ω m , with p a natural number and n≠m. Then, the governing equations are expanded
on those targeted modes, and studied via a multiple scale method [4]. This study of the equations will
allow to identify the nonlinear terms responsible of a possible exchange of energies between the
modes.
Some experiments are carried out on two rulers with piezoelectric patches in the two abovementioned
configurations (one sided and two-sided piezoelectric patches). The experiments allow us to access
some natural frequencies of the structure and their modal shapes. Displacements behaviour of modes
in internal resonance are also registered, when excited directly.
Both experiments and the theoretical studies validate that, for some specific positions of piezoelectric
patches, a 1:3 and 1:2 internal resonances are created, between the second and third frequency and
the third and fourth, respectively. However, only slight energy exchanges between those modes were
measured.
Nonlinear reduced order model of the structure are currently under investigation to understand and
possibly increase those energy exchanges.
Domaines
Mécanique [physics.med-ph]Origine | Fichiers produits par l'(les) auteur(s) |
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