A space-adiabatic theorem for longitudinal and transversal wave motion analysis of graded metamaterials
Year: 2024
Type: article
Abstract: Graded metamaterials are of great use in wave manipulation and energy harvesting fields, however, it has the drawback that after a certain amount of time, waves are reflected or trapped (rainbow effect) in some cases, which causes the scattering of energy. To solve this problem, in this work, we extend the adiabatic theorem to the spatial modulation field with the purpose of both eliminating the reflection and improving the transmission at the interface of graded metamaterials. Firstly, an analytical limiting gradient expression for the space-adiabatic theorem is derived. Then, it is applied to study the longitudinal wave motion in a spring mass with graded resonators system and the transversal wave motion in a beam with graded resonators system. It is demonstrated by numerical study that if the spatial gradient of system properties is small enough to fulfill the adiabatic theorem, the wave reflection will be eliminated and the transmission will see a drastic increase compared to the non-adiabatic case. Finally, the critical line between adiabatic and non-adiabatic cases is drawn by the fitting method. Parameter analysis shows that grading parameters and profiles play an important role in manipulating wave propagation.
Authors: Pingping Liu, Hongjun Xiang
Institution: Beijing Jiaotong University
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G3408402824, G7004085764
OpenAlex ID: W4402984541