In this paper, the focus is on the free vibrations of locally resonant metamaterial plates with viscously damped resonators. Upon formulating a dynamic-stiffness model where the resonators are represented via pertinent reaction forces depending on the deflections of the attachment points, the complex eigenvalues are calculated by a contour-integral algorithm introduced in the literature for general nonlinear eigenvalue problems. The interest in the proposed approach is twofold. The dynamic-stiffness model involves a limited number of generalised coordinates compared to the nodal degrees of freedom of a standard finite-element model, and the contour-integral algorithm proves successful in evaluating all complex eigenvalues, without missing any one, with remarkable computational efficiency. Numerical results are presented for Lévy plates, but are readily extendible to other plate theories. Finally, an ad hoc dynamic-stiffness approach is formulated to calculate the frequency response of the plate under arbitrarily placed loads, which is of particular interest to investigate its elastic wave attenuation properties.

On the Free Vibrations of Non-Classically Damped Locally Resonant Metamaterial Plates

Amendola A.;
2022

Abstract

In this paper, the focus is on the free vibrations of locally resonant metamaterial plates with viscously damped resonators. Upon formulating a dynamic-stiffness model where the resonators are represented via pertinent reaction forces depending on the deflections of the attachment points, the complex eigenvalues are calculated by a contour-integral algorithm introduced in the literature for general nonlinear eigenvalue problems. The interest in the proposed approach is twofold. The dynamic-stiffness model involves a limited number of generalised coordinates compared to the nodal degrees of freedom of a standard finite-element model, and the contour-integral algorithm proves successful in evaluating all complex eigenvalues, without missing any one, with remarkable computational efficiency. Numerical results are presented for Lévy plates, but are readily extendible to other plate theories. Finally, an ad hoc dynamic-stiffness approach is formulated to calculate the frequency response of the plate under arbitrarily placed loads, which is of particular interest to investigate its elastic wave attenuation properties.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4778631
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact