Análise de uma metaestrutura elástica com sistemas localmente ressonantes não uniformes

• Autor(a) principal: Melo, Renan Trevizan de
• Data de Publicação: 2021
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/213983
• topic: Metamaterials; Finite element analysis; Metamateriais; Análise de elementos finitos; Vibração

This work is based on the analysis of an elastic metamaterial with locally resonant systems, which consists of a cantilever beam with allocation of five equidistant resonators (spring-mass systems). Although typically the tuning (choice of natural frequencies) of these absorbers is done in a uniform way, with all of them adjusted to the same objective frequency, the aim of this study is focused on promoting non-uniform tuning. In particular, the interest in providing a reduction in the total mass added to the system stands out. Therefore, the effects of the proposed modifications on the structure's transmissibility characteristics for some cases of interest, associated with the expansion of the bandgap (vibration attenuation range observed in the metastructure transmissibility due to the allocation of resonators) are presented. For this purpose, a mathematical model referring to the equations of movement of the metamaterial in the frequency domain was implemented. This methodology made it possible to obtain the expected response for the reference case (with uniform tuning), and allowed the individual alteration of the absorber mass parameters. Furthermore, a complementary analysis via finite element methods was elaborated in order to validate the obtained results, and could also provide a practical way to validate the dynamic behavior of the structure. The individual modifications of the resonators (numbered from 1 to 5 from the base to the end of the beam) brought indications that reductions in masses 3 and 5 are more favorable in terms of bandgap enlargement. 22% magnifications were observed through 30% reductions in the masses of these resonators. It was also observed that more abrupt reductions, of 41%, in the mass in resonator 4, together with the respective reductions of 17% and 30% in resonators 3 and 5, contributed significantly to the expansion of the bandgap, which came to about 35%. Resonators 1 and 2, in turn, proved to be more susceptible to favorable contributions by reducing their objective frequency (reflected in the reduction of their stiffness). Thus, the most attractive configuration revealed a significant bandgap expansion of 85%, consisting of 36% and 19% reductions in the stiffness of absorbers 1 and 2 (with maintenance of their mass) with the most optimized configuration described for the other absorbers. Based on these results, an exponential distribution for the resonator masses was proposed, based on the most promising case, and revealed an increase, also expressive, of 71.68%. In addition, the evaluation of a sinusoidal frequency distribution of the resonators, associated with the beam's second mode of vibration, was claimed, revealing significant increases of 47.2% due to more subtle changes in the masses (whose maximum variation became 31.5%). in relation to the initial mass). It is concluded that carefully tuned resonators can significantly improve the model's response (in terms of bandgap bandwidth). In this sense, for structures with mass increase restrictions, this analysis provides a practical way to obtain wider attenuation ranges.