Bandgaps and vibration isolation of local resonance sandwich-like plate with simply supported overhanging beam

doi:10.1007/s10483-021-2790-7

Abstract

Abstract: The concept of local resonance phononic crystals proposed in recent years provides a new chance for theoretical and technical breakthroughs in the structural vibration reduction. In this paper, a novel sandwich-like plate model with local resonator to acquire specific low-frequency bandgaps is proposed. The core layer of the present local resonator is composed by the simply supported overhanging beam, linear spring and mass block, and well connected with the upper and lower surface panels. The simply supported overhanging beam is free at right end, and an additional linear spring is added at the left end. The wave equation is established based on the Hamilton principle, and the bending wave bandgap is further obtained. The theoretical results are verified by the COMSOL finite element software. The bandgaps and vibration characteristics of the local resonance sandwich-like plate are studied in detail. The factors which could have effects on the bandgap characteristics, such as the structural damping, mass of vibrator, position of vibrator, bending stiffness of the beam, and the boundary conditions of the sandwich-like plates, are analyzed. The result shows that the stopband is determined by the natural frequency of the resonator, the mass ratio of the resonator, and the surface panel. It shows that the width of bandgap is greatly affected by the damping ratio of the resonator. Finally, it can also be found that the boundary conditions can affect the isolation efficiency.

Key words: local resonance, sandwich-like plate, elastic wave bandgap, vibration isolation

2010 MSC Number:

74H45

Chenxu QIANG, Yuxin HAO, Wei ZHANG, Jinqiang LI, Shaowu YANG, Yuteng CAO. Bandgaps and vibration isolation of local resonance sandwich-like plate with simply supported overhanging beam. Applied Mathematics and Mechanics (English Edition), 2021, 42(11): 1555-1570.

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References

[1] LI, J. Q., FAN, X. L., and LI, F. M. Numerical and experimental study of a sandwich-like metamaterial plate for vibration suppression. Composite Structures, 238, 111969(2020)
[2] ZHU, J., CHRISTENSEN, J., JUNG, J., MARTIN-MORENO, L., YIN, X., FOK, L., ZHANG, X., and GARCIA-VIDAL, F. J. A holey-structured metamaterial for acoustic deep-subwavelength imaging. Nature Physics, 7(1), 52-55(2011)
[3] LAI, Y., WU, Y., SHENG, P., and ZHANG, Z. Q. Hybrid elastic solids. Nature Materials, 10, 620-624(2011)
[4] MEI, J., MA, G. C., YANG, M., YANG, Z. Y., WEN, W. J., and SHENG, P. Dark acoustic metamaterials as super absorbers for low-frequency sound. Nature Communications, 3, 756(2012)
[5] WEN, X. X., WEN, J. H., YU, D. L., WANG, G., LIU, Y. Z., and HAN, X. Y. Phononic Crystals, National Defense Industry Press, Beijing (2009)
[6] LIU, Z. Y., ZHANG, X. X., MAO, Y. W., ZHU, Y. Y., YANG, Z. Y., CHAN, C. T., and SHENG, P. Locally resonant sonic materials. Physica B:Condensed Matter, 338, 201-205(2000)
[7] LV, H. Y. and ZHANG, Y. M. A wave-based vibration analysis of a finite Timoshenko locally resonant beam suspended with periodic uncoupled force-moment type resonators. Crystals, 10, 1132(2020)
[8] CAI, C. X., WANG, Z. H., CHU, Y. Y., LIU, G. S., and XU, Z. The phononic band gaps of Bragg scattering and locally resonant pentamode metamaterials. Journal of Physics D:Applied Physics, 50, 415105(2017)
[9] NING, L., WANG, Y. Z., and WANG, Y. S. Active control of elastic metamaterials consisting of symmetric double Helmholtz resonator cavities. International Journal of Mechanical Sciences, 10, 1016(2019)
[10] HIRSEKORN, M. Small-size sonic crystals with strong attenuation bands in the audible frequency range. Applied Physics Letters, 84, 3364-3366(2004)
[11] WANG, G. Research on the Mechanism and the Vibration Attenuation Characteristic of Locally Resonant Band Gap in Phononic Crystals, Ph.D. dissertation, National Defense University of Science and Technology, Changsha (2005)
[12] PENNEC, Y., ROUHANI, B. D., LARABI, H., AKJOUJ, A., GILLET, J. N., VASSEUR, J. O., and THABET, G. Phonon transport and waveguiding in a phononic crystal made up of cylindrical dots on a thin homogeneous plate. Physical Review B, 80, 144302(2009)
[13] YU, D. Research on the Vibration Band Gaps of Periodic Beams and Plates Based on the Theory of Phononic Crystals, Ph.D. dissertation, National Defense University of Science and Technology, Changsha (2006)
[14] WANG, Y. F. and WANG, Y. S. Complete bandgaps in two-dimensional phononic crystal slabs with resonators. Journal of Applied Physics, 114, 43509(2013)
[15] ERRICO, F., TUFANO, G., ROBIN, O., GUENFOUD, N., and ATALLA, N. Simulating the sound transmission loss of complex curved panels with attached noise control materials using periodic cell wavemodes. Applied Acoustics, 156, 21-28(2019)
[16] OUDICH, M., LI, Y., ASSOUAR, B. M., and HOU, Z. A sonic band gap based on the locally resonant phononic plates with stubs. New Journal of Physics, 12, 083049(2010)
[17] MA, F. Y., XU, Y. C., and WU, J. H. Modal displacement method for extracting the bending wave bandgap of plate-type acoustic metamaterials. Applied Physics Express, 12, 074004(2019)
[18] MI, Y. Z., YANG, H. S., LEI, B., and ZHENG, H. A variational method for band-gap analysis of metamaterial plates with local resonators. Acta Acustica, 45, 404-414(2020)
[19] HUANG, T. Y., SHEN, C., and JING, Y. Membrane- and plate-type acoustic metamaterials. The Journal of the Acoustical Society of America, 139, 3240-3250(2016)
[20] ZHU, X. X., XIAO, Y., WEN, J. H., and YU, D. L. Flexural wave band gaps and vibration reduction properties of a locally resonant stiffened plate. Acta Physica Sinica, 17, 176202(2016)
[21] OUDICH, M., SENESI, M., ASSOUAR, M. B., RUZENNE, M., SUN, J. H., VINCENT, B., HOU, Z., and WU, T. T. Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates. Physical Review B, 84, 165136(2011)
[22] XIAO, Y. Locally Resonant Structures:Band Gap Tuning and Properties of Vibration and Noise Reduction, Ph.D. dissertation, National Defense University of Science and Technology, Changsha (2012)
[23] LU, Z. Q., SHAO, D., FANG, Z. W., DING, H., and CHEN, L. Q. Integrated vibration isolation and energy harvesting via a bi-stable piezo-composite plate. Journal of Vibration and Control, 26, 779-789(2020)
[24] LU, Z. Q., WU, D., DING, H., and CHEN, L. Q. Vibration isolation and energy harvesting integrated in a Stewart platform with high static and low dynamic stiffness. Applied Mathematical Modelling, 89, 249-267(2021)
[25] SONG, Y., FENG, L., WEN, J., YU, D., and WEN, X. Reduction of the sound transmission of a periodic sandwich-like plate using the stop band concept. Composite Structures, 128, 428-436(2015)
[26] LU, Z. Q., ZHAO, L., DING, H., and CHEN, L. Q. A dual-functional metamaterial for integrated vibration isolation and energy harvesting. Journal of Sound and Vibration, 509, 116251(2021)
[27] LIU, Z. B., RUMPLER, R., and FENG, L. P. Broadband locally resonant metamaterial sandwichlike plate for improved noise insulation in the coincidence region. Composite Structures, 200, 165-172(2018)
[28] HE, Z. C., XIAO, X., and LI, E. Design for structural vibration suppression in laminate acoustic metamaterials. Composites Part B:Engineering, 131, 237-252(2017)
[29] QIN, Q., SHENG, M. P., and GUO, Z. W. Low-frequency vibration and radiation performance of a locally resonant plate attached with periodic multiple resonators. Applied Sciences, 10, 2843(2020)