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              <p>The aim of the work is to control the vibrations or to harvest some vibratory energy from a nonlinearstructure through modal energy exchanges of the system. To exchange energy within modes, internalresonances between them are created [1]. We then intend to design the exchange of energy, thanks tothe 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 piezoelectricmaterials, at certain positions on the beam, is studied. Two configurations are studied: the first onewith a piezoelectric patch on one side on top of the elastic beam, and the second one with twocollocated patches. Those two configurations have different effects on the nonlinear terms, becauseof the axial symmetry or asymmetry it creates. We write the governing nonlinear equations of thesystem, supposing an Euler Bernoulli beam with large deformations. The nonlinearities of the modelcome from the large rotation nonlinearity of the beam [2] and the assumption of a nonlinear materialbehaviour of the piezoelectric patches [3].The positions of the piezoelectric patches are used to create the intended internal resonance. Writtenin a general manner, the n th and the m th frequencies (ω n and ω m , respectively) are in internalresonance if ω n ≈p ω m , with p a natural number and n≠m. Then, the governing equations are expandedon those targeted modes, and studied via a multiple scale method [4]. This study of the equations willallow to identify the nonlinear terms responsible of a possible exchange of energies between themodes.Some experiments are carried out on two rulers with piezoelectric patches in the two abovementionedconfigurations (one sided and two-sided piezoelectric patches). The experiments allow us to accesssome natural frequencies of the structure and their modal shapes. Displacements behaviour of modesin internal resonance are also registered, when excited directly.Both experiments and the theoretical studies validate that, for some specific positions of piezoelectricpatches, a 1:3 and 1:2 internal resonances are created, between the second and third frequency andthe third and fourth, respectively. However, only slight energy exchanges between those modes weremeasured.Nonlinear reduced order model of the structure are currently under investigation to understand andpossibly increase those energy exchanges.</p>
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