Abstract
The bimodal quarter-wave impedance matching theory, with which an incident longitudinal (transverse) wave can be completely converted to a transmitted transverse (longitudinal) wave, requires that the matching element must exhibit specific anisotropy. Previously, the specific anisotropy was satisfied between components of the stiffness tensor, and the phenomenon was only realized in the ultrasonic frequency range. In this work, we find that such anisotropy can also be satisfied between components of the mass density tensor, which allows an ultralow frequency realization. Meanwhile, the stiffness should also exhibit special anisotropy. To meet such unique anisotropy, we propose to design ternary locally resonant metamaterials. The dipolar local resonance around the lowest bandgap allows us to deal with the effective stiffness and mass density separately. The requirement on stiffness is satisfied by designing the matrix, and the mass anisotropy is realized through design of the coating layer. With the designed metamaterials, the matching elements can convert wave modes, which have a wavelength much larger than the element’s width. Considering that mode conversion is a fundamental phenomenon in the elastic field, our finds and design can be critically useful to extend its application in the ultralow frequency range.
Highlights
As a well-known phenomenon in the elastic field, mode conversion between longitudinal (L) and transverse (T) wave modes fundamentally changes how a wave propagates and, is quite useful in various industrial applications, such as nondestructive inspection,1 medical imagination,2 and vibration attenuation.The traditional method is to design a wedge-type modeconvertor based on Snell’s law that can only realize a very low modeconverting efficiency
Mass anisotropy, which can be realized based on the local resonance mechanism, allows us to realize the mode conversion phenomenon in the ultralow frequency range
We re-examine the theoretical conditions based on mass anisotropy
Summary
As a well-known phenomenon in the elastic field, mode conversion between longitudinal (L) and transverse (T) wave modes fundamentally changes how a wave propagates and, is quite useful in various industrial applications, such as nondestructive inspection, medical imagination, and vibration attenuation.The traditional method is to design a wedge-type modeconvertor based on Snell’s law that can only realize a very low modeconverting efficiency. Perfect transmodal Fabry–Perot interference (TFPI) theory and bimodal quarter-wave impedance matching theory were later proposed, and both of them can realize quite high mode-converting efficiencies. With the former theory, an incident L (T) wave can be solely and maximally converted to a transmitted T (L) wave; with the latter one, a nearly complete mode-converting transmission can be achieved. In this work, we aim to explore whether it is possible to realize a high mode-converting transmission efficiency with mass anisotropy. Such an investigation could be quite useful for mode conversion application in ultralow frequency ranges. We will consider the bi-modal quarter-wave impedance matching theory in this work
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