Journal of Vibration Testing and System Dynamics
Hermitian Symmetry of a Dynamic Structure with Odd Elasticity
Journal of Vibration Testing and System Dynamics 9(1) (2025) 89--95 | DOI:10.5890/JVTSD.2025.03.006
Z.C. Feng
Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
Download Full Text PDF
Abstract
We present the wing flutter model as a dynamic structure with odd elasticity. The wing flutter model is an elastically supported airfoil in the flow. The lift force contributes to the non-Hermitian stiffness to the existing elastic support. The stability analysis of the flutter model demonstrates the onset of oscillations due to the odd elasticity. Surprisingly, we found linear coordinate transformations such that the equations of motion in the new coordinates are Hermitian: with symmetric mass matrix and symmetric stiffness matrix.
References
-
[1]  | Scheibner, C., Souslov, A., Banerjee, D., Surowka, P., Irvine, W.T., and Vitelli, V. (2020), Odd elasticity, Nature Physics, 16(4), 475-480.
|
-
[2]  | Yasuda, K., Hosaka, Y., Sou, I., and Komura, S. (2021), Odd microswimmer, Journal of the Physical Society of Japan, 90(7), p.075001.
|
-
[3]  | Chen, Y., Li, X., Scheibner, C., Vitelli, V., and Huang, G. (2021), Realization of active metamaterials with odd micropolar elasticity,
Nature Communications, 12(1), p.5935.
|
-
[4]  | Ishimoto, K., Moreau, C., and Yasuda, K. (2022), Self-organized swimming with odd elasticity, Physical Review E, 105(6), p.064603.
|
-
[5]  | Wu, Q. (2022), A Study of Unprecedented Wave Control with Active Elastic Metamaterials, PhD Thesis, University of Missouri, Columbia.
|
-
[6]  | Brandenbourger, M., Locsin, X., Lerner, E., and Coulais, C. (2019), Non-reciprocal robotic metamaterials, Nature Communications,
10(1), p.4608.
|
-
[7]  | Nassar, H., Yousefzadeh, B., Fleury, R., Ruzzene, M., Alu, A., Daraio, C., Norris, A.N., Huang, G., and Haberman, M.R. (2020), Nonreciprocity in acoustic and elastic materials, Nature Reviews Materials, 5(9), 667-685.
|
-
[8]  | Blevins, R.D. (1990), Flow-Induced Vibration: $2^{nd}$ edition, Van Nostrand Reinhold, New York.
|