Elusive isolating frequency of a locally resonant mechanical meta-layer

In this work, we report a meta-layer consisting of subwavelength local resonators to achieve low-frequency isolation of elastic waves. Apart from its distinctive low-dimensional configuration with a thickness of 17 the wavelength, the meta-layer differs from bandgap-based metamaterials in that its optimally isolating frequency is higher than the eigenfrequency. We demonstrate theoretically, numerically, and experimentally that the isolating frequency shift arises from the coupling effect between the resonators and the load-carrying plate or beam. As a further step, to demonstrate the universality of our theory, we predict and design a meta-layer with an opposite-frequency shift. The proposed meta-layer, along with its corresponding theory, can precisely guide the development of compact low-frequency wave isolation devices.