Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

doi:10.1007/s10483-023-2978-7

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (4): 515-524.doi: https://doi.org/10.1007/s10483-023-2978-7

• 论文 • 下一篇

Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

Shengjie YAO, Yijun CHAI, Xiongwei YANG, Yueming LI

State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China

收稿日期:2022-10-31 修回日期:2023-01-07 出版日期:2023-04-01 发布日期:2023-03-30
通讯作者: Xiongwei YANG, E-mail: op.yangxw@xjtu.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. U2033208 and 52192633), the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2021JQ006), the China Postdoctoral Science Foundation (No. 2020TQ0241), and the Innovative Scientific Program of China Nuclear Power Engineering Co., Ltd.

Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

Shengjie YAO, Yijun CHAI, Xiongwei YANG, Yueming LI

State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China

Received:2022-10-31 Revised:2023-01-07 Online:2023-04-01 Published:2023-03-30
Contact: Xiongwei YANG, E-mail: op.yangxw@xjtu.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. U2033208 and 52192633), the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2021JQ006), the China Postdoctoral Science Foundation (No. 2020TQ0241), and the Innovative Scientific Program of China Nuclear Power Engineering Co., Ltd.

摘要/Abstract

摘要： In this work, we design a twisting metamaterial for longitudinal-torsional (L-T) mode conversion in pipes through exploring the theory of perfect transmodal Fabry-Perot interference (TFPI). Assuming that the axial and radial motions in pipes can be decoupled, we find that the metamaterial can be designed in a rectangular coordinate system, which is much more convenient than that in a cylindrical system. Numerical calculation with detailed microstructures shows that an efficient L-T mode conversion can be obtained in pipes with different radii. In addition, we fabricate mode-converting microstructures on an aluminum pipe and conduct ultrasonic experiments, and the results are in good agreement with the numerical calculations. We expect that the proposed L-T mode-converting metamaterial and its design methodology can be applied in various ultrasonic devices.

关键词: elastic wave, mode conversion, elastic metamaterial, ultrasonic device

Abstract: In this work, we design a twisting metamaterial for longitudinal-torsional (L-T) mode conversion in pipes through exploring the theory of perfect transmodal Fabry-Perot interference (TFPI). Assuming that the axial and radial motions in pipes can be decoupled, we find that the metamaterial can be designed in a rectangular coordinate system, which is much more convenient than that in a cylindrical system. Numerical calculation with detailed microstructures shows that an efficient L-T mode conversion can be obtained in pipes with different radii. In addition, we fabricate mode-converting microstructures on an aluminum pipe and conduct ultrasonic experiments, and the results are in good agreement with the numerical calculations. We expect that the proposed L-T mode-converting metamaterial and its design methodology can be applied in various ultrasonic devices.

Key words: elastic wave, mode conversion, elastic metamaterial, ultrasonic device

中图分类号:

74K25

Shengjie YAO, Yijun CHAI, Xiongwei YANG, Yueming LI. Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(4): 515-524.

参考文献

[1] SU, X. S., LU, Z. C., and NORRIS, A. N. Elastic metasurfaces for splitting SV- and P-waves in elastic solids. Journal of Applied Physics, 123(9), 091701(2018)
[2] ZHENG, M. Y., PARK, C. I., LIU, X. N., ZHU, R., and HU, G. K. Non-resonant metasurface for broadband elastic wave mode splitting. Applied Physics Letters, 116(17), 171903(2020)
[3] WU, Y., LAI, Y., and ZHANG, Z. Q. Elastic metamaterials with simultaneously negative effective shear modulus and mass density. Physical Review Letters, 107(10), 105506(2011)
[4] GUSEV, V. E. and WRIGHT, O. B. Double-negative flexural acoustic metamaterial. New Journal of Physics, 16(12), 123053(2014)
[5] LEE, H., OH, J. H., SEUNG, H. M., CHO, S. H., and KIM, Y. Y. Extreme stiffness hyperbolic elastic metamaterial for total transmission subwavelength imaging. Scientific Reports, 6, 24026(2016)
[6] DING, Y. H., STATHARAS, E. C., YAO, K., and HONG, M. H. A broadband acoustic metamaterial with impedance matching layer of gradient index. Applied Physics Letters, 110(24), 241903(2017)
[7] WANG, Y. Z., LI, F. M., and WANG, Y. S. Active feedback control of elastic wave metamaterials. Journal of Intelligent Material Systems and Structures, 28(15), 2110-2116(2017)
[8] NING, L., WANG, Y. Z., and WANG, Y. S. Active control of a black hole or concentrator for flexural waves in an elastic metamaterial plate. Mehanics of Materials, 142, 103300(2020)
[9] ZHU, R., LIU, X. N., HU, G. K., SUN, C. T., and HUANG, G. L. Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial. Nature Communications, 5, 5510(2014)
[10] KWEUN, J. M., LEE, H. J., OH, J. H., SEUNG, H. M., and KIM, Y. Y. Transmodal Fabry-Perot resonance: theory and realization with elastic metamaterials. Physical Review Letters, 118(20), 205901(2017)
[11] YANG, X. W., KWEUN, J. M., and KIM, Y. Y. Theory for perfect transmodal Fabry-Perot interferometer. Scientific Reports, 8, 69(2018)
[12] YANG, X. W. and KIM, Y. Y. Asymptotic theory of bimodal quarter-wave impedance matching for full mode-converting transmission. Physical Review B, 98(14), 144110(2018)
[13] YANG, X. W. and KIM, Y. Y. Topology optimization for the design of perfect mode-converting anisotropic elastic metamaterials. Composite Structures, 201, 161-177(2018)
[14] YANG, X. W., CHAI, Y. J., and LI, Y. M. Metamaterial with anisotropic mass density for full mode-converting transmission of elastic waves in the ultralow frequency range. AIP Advances, 11(12), 125205(2021)
[15] YANG, X. W., CHAI, Y. J., GENG, Q., and LI, Y. M. Inverse design of locally resonant metamaterial with anisotropic mass density for perfect transmodal Fabry-Perot interference. Journal of Applied Physics, 129(21), 215103(2021)
[16] YANG, X. W., WANG, T., CHAI, Y. J., and LI, Y. M. Fiber-reinforced composite metamaterials for mode conversion of elastic waves. Journal of Physics D: Applied Physics, 55(3), 035302(2022)
[17] KIM, M. S., LEE, W. R., KIM, Y. Y., and OH, J. H. Transmodal elastic metasurface for broad angle total mode conversion. Applied Physics Letters, 112(24), 241905(2018)
[18] LEE, S. W., SEUNG, H. M., CHOI, W., KIM, M., and OH, J. H. Broad-angle refractive transmodal elastic metasurface. Applied Physics Letters, 117(21), 213502(2020)
[19] KANNAN, E., MAXFIELD, B. W., and BALASUBRAMANIAM, K. SHM of pipes using torsional waves generated by in situ magnetostrictive tapes. Smart Materials and Structures, 16(6), 2505-2515(2007)
[20] CHO, S. H., KIM, H. W., and KIM, Y. Y. Megahertz-range guided pure torsional wave transduction and experiments using a magnetostrictive transducer. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 57(5), 1225-1229(2010)
[21] KIM, Y. G., MOON, H. S., PARK, K. J., and LEE, J. K. Generating and detecting torsional guided waves using magnetostrictive sensors of crossed coils. NDT & E International, 44, 145-151(2011)
[22] KIM, Y. Y. and KWON, Y. E. Review of magnetostrictive patch transducers and applications in ultrasonic nondestructive testing of waveguides. Ultrasonics, 62, 3-19(2015)
[23] LIU, Z. H., FAN, J. W., HU, Y. A., HE, C. F., and WU, B. Torsional mode magnetostrictive patch transducer array employing a modified planar solenoid array coil for pipe inspection. NDT & E International, 69, 9-15(2015)
[24] LIN, S. Study on the longitudinal-torsional composite transducer with slanting slots. Acta Acustica, 24(1), 59-65(1999)
[25] PI, J. Longitudinal-torsional vibration converter of cylinder with multiple diagonal slits. Chinese Journal of Mechanical Engineering, 44(5), 242-248(2008)
[26] ASAMI, T. and MIURA, H. Vibrator development for hole machining by ultrasonic longitudinal and torsional vibration. Japanese Journal of Applied Physics, 50(7), 07he31(2011)
[27] CHEN, T., LIU, S. L., LIU, W., and WU, C. Q. Study on a longitudinal-torsional ultrasonic vibration system with diagonal slits. Advances in Mechanical Engineering, 9(7), 7-10(2017)
[28] YUAN, S., TANG, Z., WU, Q., and SONG, H. Design of longitudinal torsional ultrasonic transducer and its performance test. Journal of Mechanical Engineering, 55(1), 139-148(2019)
[29] GU, L., ZHENG, K., and DONG, S. Design of miniature longitudinal-torsional ultrasonic machining system. Journal of Nanjing University of Science and Technology, 44(2), 127-133(2020)
[30] FRENZEL, T., KADIC, M., and WEGENER, M. Three-dimensional mechanical metamaterials with a twist. Science, 358(6366), 1072-1074(2017)
[31] XU, Z. L., WANG, D. F., TACHI, T., and CHUANG, K. C. An origami longitudinal-torsional wave converter. Extreme Mechanics Letters, 51, 101570(2021)
[32] GUEDES, J. M. and KIKUCHI, N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element method. Computer Methods in Applied Mechanics and Engineering, 83(2), 143-198(1990)

Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

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