Abstract
Locally resonant metamaterial plates with subwavelength bandgaps can be exploited for the simultaneous control of structural vibrations and acoustic radiation. The present work theoretically investigates the vibroacoustic characteristics of a metamaterial plate with periodic lateral local resonance. The high accuracy of the presented method is evident from the consistency of the cross mobility of the metamaterial plate calculated with the finite element technique. The modal superposition approach and Rayleigh integral technique are adopted to formulate the mean square velocity and acoustic radiation power in terms of the structural deflection and sound pressure to capture the vibroacoustic coupling characteristics of the metamaterial plate and the surrounding environment. Large vibration suppression and sound reduction with high radiation efficiency can be observed within the frequency ranges of interest. The near-field sound intensity and far-field acoustic pressure distributions inside and outside the bandgaps are plotted and analyzed. The results from this work can be utilized to set design guidelines for metamaterial design to achieve prescribed vibroacoustic characteristics.
Similar content being viewed by others
References
Shaat M, El Dhaba AR. On the equivalent shear modulus of composite metamaterials. Compos Part B-Eng. 2019;172:506–15.
Wu K, Hu H, Wang L. Experimental study on wave propagation in one-dimensional viscoelastic metamaterial. Acta Mech Solida Sin. 2021;34:597–611.
Jung J, Kim HG, Goo S, Chang KJ, Wang S. Realisation of a locally resonant metamaterial on the automobile panel structure to reduce noise radiation. Mech Syst Signal Pr. 2019;122:206–31.
Lin Q, Zhou J, Pan H, Xu D, Wen G. Numerical and experimental investigations on tunable low-frequency locally resonant metamaterials. Acta Mech Solida Sin. 2021;34:612–23.
Wang T. Tunable band gaps in an inertant metamaterial plate with two-degree-of-freedom local resonance. Phys Lett A. 2020;384:126420.
Huang H, Sun C. Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density. New J Phys. 2009;11:013003.
Huang H, Sun C. Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young’s modulus. J Mech Phys Solids. 2011;59:2070–81.
Su YC, Sun CT. Design of double negativity elastic metamaterial. Int J Smart Nano Mat. 2015;6:61–72.
Man X, Luo Z, Liu J, Xia B. Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale. Mater Design. 2019;180:107911.
Wang H, Zhang Y, Lin W, Qin Q-H. A novel two-dimensional mechanical metamaterial with negative Poisson’s ratio. Comp Mater Sci. 2020;171:109232.
Xiao Y, Wen J, Wen X. Flexural wave band gaps in locally resonant thin plates with periodically attached spring–mass resonators. J Phys D Appl Phys. 2012;45:195401.
Gusev VE, Wright OB. Double-negative flexural acoustic metamaterial. New J Phys. 2014;16:123053.
Linzhongyang E, Chen Z, Li F, Zou G. Band-gap properties of elastic sandwich metamaterial plates with composite periodic rod core. Acta Mech Solida Sin. 2021;35:51–62.
He ZH, Wang YZ, Wang YS. Sound transmission comparisons of active elastic wave metamaterial immersed in external mean flow. Acta Mech Solida Sin. 2021;34:307–25.
Wang T, Sheng M, Ding X, Yan X. Wave propagation and power flow in an acoustic metamaterial plate with lateral local resonance attachment. J Phys D Appl Phys. 2018;51:115306.
He ZH, Wang YZ, Wang YS. External mean flow on sound radiation of active mechanical metamaterials. AIAA J. 2020;58:4751–63.
Hoang T, Duhamel D, Foret G. Wave finite element method for waveguides and periodic structures subjected to arbitrary loads. Finite Elem Anal Des. 2020;179:103437.
Liu J, Guo H, Wang T. A review of acoustic metamaterials and phononic crystals. Curr Comput-Aided Drug Des. 2020;10:305.
Wang T, Sheng MP, Guo ZW, Qin QH. Flexural wave suppression by an acoustic metamaterial plate. Appl Acoust. 2016;114:118–24.
Wang T, Sheng M, Qin Q. Sound transmission loss through metamaterial plate with lateral local resonators in the presence of external mean flow. J Acoust Soc Am. 2017;141:1161–9.
Xiao Y, Wen J, Wen X. Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators. J Sound Vib. 2012;331:5408–23.
Wang T, Sheng MP, Guo ZW, Qin QH. Acoustic characteristics of damped metamaterial plate with parallel attached resonators. Arch Mech. 2017;69:29–52.
Song Y, Feng L, Liu Z, Wen J, Yu D. Suppression of the vibration and sound radiation of a sandwich plate via periodic design. Int J Mech Sci. 2019;150:744–54.
He ZH, Wang YZ, Wang YS. Active feedback control on sound radiation of elastic wave metamaterials. AIAA J. 2019;57:4536–47.
Guo Z, Sheng M, Pan J. Vibro-acoustic performance of a sandwich plate with periodically inserted resonators. Appl Sci. 2019;9:3651–73.
Frank Fahy PG. Sound and structural vibration radiation, transmission and response. Oxford: Elsevier; 2007.
Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 52001131 and No. 52071152).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Rights and permissions
About this article
Cite this article
Wang, T., Guo, H., Chen, M. et al. Theoretical Modeling and Analysis of Vibroacoustic Characteristics of an Acoustic Metamaterial Plate. Acta Mech. Solida Sin. 35, 775–786 (2022). https://doi.org/10.1007/s10338-022-00320-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10338-022-00320-9