Predicting the stop-band behaviour of finite mono-coupled periodic structures from the transmissibility of a single element

Autor(es)

Goncalves, P. J. P. ^[1] ; Brennan, M. J. ^[2] ; Cleante, V. G. ^[2]

Afiliação do(s) autor(es)

^[1] State Univ Sao Paulo, Sch Engn, UNESP, Bauru, SP - Brazil

^[2] State Univ Sao Paulo, Sch Engn, UNESP, Ilha Solteira - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MECHANICAL SYSTEMS AND SIGNAL PROCESSING; v. 154, JUN 1 2021.
• Citações Web of Science: 1

Resumo

The study of mono-coupled periodic structures has gained renewed interest by the scientific community due to the new applications of metamaterials and meta-structures. Much research has focused on the wave propagation properties of infinite structures. However, this paper focuses on finite periodic structures, in particular the parameters that govern the behaviour of a low frequency stop-band of such a structure. From an engineering perspective, these are the lower and upper cut-off frequencies, i.e., the bandwidth, and the minimum transmission of vibration within the band. Using the Caley-Hamilton theorem, analytical expressions are derived for the receptance, dynamic stiffness and transmissibility of a finite mono-coupled structure. It is shown that the properties of the whole structure can be determined from the transmissibility of a single element. If the element is symmetric, then the expressions describing the stop-band are particularly simple. An approximate analytical expression has been derived that allows the number of elements needed for a given maximum attenuation in a low frequency stop-band to be determined. To illustrate the approach, lumped parameter systems are considered, in which the stop-band behaviour is governed by the addition of mass, stiffness and a vibration absorber. Expressions are derived for the maximum vibration attenuation within the first stop-band, for each case, enabling clear physical insight into the controlling parameters. Expressions are provided for the lower and upper cut-off frequencies of the stop-band. Some experimental results are also presented to support the theoretical analysis. (C) 2020 Elsevier Ltd. All rights reserved. (AU)

• Processo FAPESP: 18/15894-0 - Projeto e otimização de estruturas periódicas para aprimoramento de desempenho vibroacústico
• Beneficiário: Carlos de Marqui Junior
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 20/00659-6 - Análise experimental de estruturas periódicas não-lineares
• Beneficiário: Vinícius Germanos Cleante
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado