Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
On the design of nonlinear resonators to improve the displacement transmissibility of mono-coupled periodic rod structures
Submission Author:
Felipe Anezio , SP
Co-Authors:
Felipe Anezio, Paulo José Paupitz Gonçalves, Douglas Roca Santo, Leopoldo de Oliveira
Presenter: Paulo José Paupitz Gonçalves
doi://10.26678/ABCM.COBEM2023.COB2023-0784
Abstract
Recent studies have demonstrated that vibration reduction can be obtained by using the concept of periodicity. The study of periodic structures is closely linked to the field of metamaterials, which are materials that exhibit spatial periodicity. The concept involves the assembling of repetitive of unit cell elements to form a whole structure. When elastic waves propagate through these structures, they are reshaped, resulting in frequency intervals where the waves cannot freely propagate, known as bandgaps. A key idea in this research is to model a unitary cell of the periodic structure with a non-linear resonator attachment. The resonant frequencies of a structure coupled to non-linear springs depend on the displacement levels, which can be translated into a broadening frequency range. This makes the non-linear response interesting as the effect of grading metamaterials is achieved due to the different levels each resonator vibrates. The Harmonic Balance analytical method is used to produce an approximate polynomial equation for accurately calculating frequency response functions (FRFs). Comparisons were made with numerical solutions, integrating displacements using the Runge-Kutta method and implementing a finite element model. These methods serve as a source of comparison for demonstrating the accuracy of the results. Initially, the linear case was discussed to observe the effects of the linear resonator. When the non-linear spring is considered, the displacement transmissibility shows an increase in the bandgap region, where three possible responses also occurred, compared to the purely linear resonator. The effect of the hardening spring on some resonance peaks is known, with the resonance peaks bending to higher frequencies. The non-linear stiffness associated with the added vibration absorber changed the dynamic behavior of the device, generating some advantages at lower frequencies, allowing for a reduction in mass. When comparing with the linear case, the non-linear resonator causes the enlargement of the attenuation band. These findings open interesting perspectives on vibration control in periodic structures connected to non-linear resonators.
Keywords
periodic structures, Resonant Metamaterial, Non-linear analysis, Vibration control
