Locally resonant plate model considering the rotation coupling effect

doi:10.1007/s10483-026-3344-7

Abstract

Abstract:

In this paper, a theoretical model is established for locally resonant plates with general resonators, and the corresponding governing equation is derived. The model provides a mathematical demonstration of the locally resonant effect, which contains two parts: the first part is induced by translation coupling, and the second part is induced by rotation coupling. The second part cannot be reflected by most existing theoretical models. The analytical solutions of the dynamic response are compared with the direct numerical simulation (DNS) results for two locally resonant plates with different resonator types, thereby validating the general applicability of the present model. The rotation coupling effect leads to the frequency-dependent effective rotational inertia density and anisotropic dispersion relation of the locally resonant plate, as well as the enhancement of the structural vibration suppression ability.

Key words: metamaterial, locally resonant plate, vibration suppression, rotation coupling

2010 MSC Number:

O347

Hefan DONG, Linjuan WANG. Locally resonant plate model considering the rotation coupling effect. Applied Mathematics and Mechanics (English Edition), 2026, 47(2): 369-388.

TrendMD

Figures/Tables 9

Fig. 1

Fig. 2

Fig. 3

Table 1

Normalized coupling inertias of the cantilever resonator"

Parameter	$Q 1$	$Q 2$	$Q 1 y R$	$Q 2 y R$	$Q 1 z R$	$Q 2 z R$
Value	0.719 59	$− 1.346 1 × 10 − 7$	0.968 17	$3.134 2 × 10 − 7$	$− 3.655 3 × 10 − 7$	0.932 02

Table 1

Fig. 4

Fig. 5

Fig. 6

Table 2

Normalized coupling inertias of the multi-beam resonator"

Parameter	Value	Parameter	Value	Parameter	Value
$Q 1$	0.414 24	$Q 1 y R$	0.790 89	$Q 2 z R$	0.898 17
$Q 3$	0.596 99	$Q 3 y R$	0.084 292	$Q 4 z R$	0.130 83
$Q 5$	0.383 78	$Q 5 y R$	0.435 73	$Q 7 z R$	0.242 28
$Q 6$	0.024 479	$Q 6 y R$	0.323 98	$Q 8 z R$	0.167 28

Table 2

Fig. 7

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