Design of Locally Resonant Damped Plates
DOI:
https://doi.org/10.70567/mc.v41i8.40Keywords:
locally resonant plates, damped resonators, design, bandgapsAbstract
A method is presented to study the dynamics of locally resonant structures, consisting of a plate with a set of periodically distributed graded elastic resonators attached. The mathematical model of such a locally resonant structure is represented by a plate, formulated by means of Mindlin's theory, coupled with a continuous distribution of mass-spring-damper systems. A modal analysis of the governing equations is performed in terms of eigenfunctions corresponding to the host plate (without resonators). A criterion to define the bandgaps of these finite structures is presented as those frequency ranges in which all modal amplification factors are less than one. Simple formulas are proposed for the pre-design of the stiffness, mass, and damping of the resonator system in order to broaden the attenuation range around a target frequency.
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