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A lattice metamaterial-based sandwich cylindrical system for numerical simulation approach of vibroacoustic transmission considering triply periodic minimal surface
Received date: 2025-05-06
Revised date: 2025-09-16
Online published: 2025-10-29
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This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system (TPMS-SCS) for the first time. Although these structures exhibit outstanding physical and mechanical properties, their dynamic and acoustic features have not been reported yet. This study addresses this gap by calculating the sound transmission loss (STL) coefficient within the framework of the wave approach across various architectures, including the primitive (P), Schoen gyroid (G), and wrapped package-graph (IWP) of a TPMS lattice structure. To determine an analytical STL, a third-order approach is used to precisely capture the stress-strain distribution based on the thickness coordinate, thereby providing a simultaneous solution to the general characteristic relations along with fluid-structure coupling. Given the lack of studies for frequency and STL comparisons, the structure is modeled considering a finite element (FE) design, which is a challenging and time-consuming process because of the complex topological TPMS configurations incorporated within a sandwich cylinder. In fact, achieving convincing computational accuracy requires fine mesh discretization, which significantly increases computational costs during vibroacoustic analysis. Using the numerical results from the COMSOL software Multiphysics, the accuracy of the analytical STL spectrum is verified for different configurations, including P, G, and IWP. The effective acoustic specifications of a TPMS-SCS in the frequency domain are examined by the comparison of the STL with that of a simple cylinder of the same mass. In this context, it would also be beneficial to examine the effect of TPMS thickness, which can demonstrate the importance of the present results. The findings of this approach can be beneficial for scholars working on the numerical and analytical sound insulation characteristics of metamaterial-based cylindrical systems.
M. R. ZARASTVAND , E. ABDOLI , R. TALEBITOOTI . A lattice metamaterial-based sandwich cylindrical system for numerical simulation approach of vibroacoustic transmission considering triply periodic minimal surface[J]. Applied Mathematics and Mechanics, 2025 , 46(11) : 2035 -2054 . DOI: 10.1007/s10483-025-3314-9
| [1] | MA, K. and BAZILEVS, Y. Isogeometric analysis of architected materials and structures. Engineering with Computers, 40, 3389–3403 (2024) |
| [2] | GANDY, P. J. and KLINOWSKI, J. Exact computation of the triply periodic G (gyroid’) minimal surface. Chemical Physics Letters, 321, 363–371 (2000) |
| [3] | GANDY, P. J. F., CVIJOVI?, D., MACKAY, A. L., and KLINOWSKI, J. Exact computation of the triply periodic D (diamond’) minimal surface. Chemical Physics Letters, 314, 543–551 (1999) |
| [4] | LI, S. H., JIANG, W. C., ZHU, X. L., and XIE, X. F. Effect of localized defects on mechanical and creep properties for pyramidal lattice truss panel structure by analytical, experimental and finite element methods. Thin-Walled Structures, 170, 108531 (2022) |
| [5] | ASADI JAFARI, M. H., ZARASTVAND, M. R., and ZHOU, J. H. Doubly curved truss core composite shell system for broadband diffuse acoustic insulation. Journal of Vibration and Control, 30, 4035–4051 (2024) |
| [6] | ZHANG, Z. J., ZHANG, Q. C., HUANG, L., ZHANG, D. Z., and JIN, F. Effect of elevated temperature on the out-of-plane compressive properties of nickel based pyramidal lattice truss structures with hollow trusses. Thin-Walled Structures, 159, 107247 (2021) |
| [7] | BIOT, M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid, I. low frequency range. The Journal of the Acoustical Society of America, 28, 168–178 (1956) |
| [8] | BIOT, M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid. II, higher frequency range. The Journal of the Acoustical Society of America, 28, 179–191 (1956) |
| [9] | BOLTON, J. S., SHIAU, N. M., and KANG, Y. J. Sound transmission through multi-panel structures lined with elastic porous materials. Journal of Sound and Vibration, 191, 317–347 (1996) |
| [10] | LEE, J. H. and KIM, J. Simplified method to solve sound transmission through structures lined with elastic porous material. The Journal of the Acoustical Society of America, 110, 2282–2294 (2001) |
| [11] | KUMAR, R. and HUNDAL, B. S. Symmetric wave propagation in a fluid-saturated incompressible porous medium. Journal of Sound and Vibration, 288, 361–373 (2005) |
| [12] | UMNOVA, O., ATTENBOROUGH, K., and LINTON, C. M. Effects of porous covering on sound attenuation by periodic arrays of cylinders. The Journal of the Acoustical Society of America, 119, 278–284 (2006) |
| [13] | DANESHJOU, K., RAMEZANI, H., and TALEBITOOTI, R. Wave transmission through laminated composite double-walled cylindrical shell lined with porous materials. Applied Mathematics and Mechanics (English Edition), 32(6), 701–718 (2011) https://doi.org/10.1007/s10483-011-1450-9 |
| [14] | ZHOU, J., BHASKAR, A., and ZHANG, X. The effect of external mean flow on sound transmission through double-walled cylindrical shells lined with poroelastic material. Journal of Sound and Vibration, 333, 1972–1990 (2014) |
| [15] | GAO, W. Y., CUI, Z. W., and WANG, K. X. Wave propagation in poroelastic hollow cylinder immersed in fluid with seismoelectric effect. Journal of Sound and Vibration, 332, 5014–5028 (2013) |
| [16] | RAMEZANI, H. and SAGHAFI, A. Optimization of a composite double-walled cylindrical shell lined with porous materials for higher sound transmission loss by using a genetic algorithm. Mechanics of Composite Materials, 50, 71–82 (2014) |
| [17] | LIU, Y. and HE, C. Analytical modelling of acoustic transmission across double-wall sandwich shells: effect of an air gap flow. Composite Structures, 136, 149–161 (2016) |
| [18] | LIU, Y. and HE, C. B. On sound transmission through double-walled cylindrical shells lined with poroelastic material: comparison with Zhou’s results and further effect of external mean flow. Journal of Sound and Vibration, 358, 192–198 (2015) |
| [19] | ZHOU, J., BHASKAR, A., and ZHANG, X. Sound transmission through double cylindrical shells lined with porous material under turbulent boundary layer excitation. Journal of Sound and Vibration, 357, 253–268 (2015) |
| [20] | LIU, Y. and HE, C. B. Diffuse field sound transmission through sandwich composite cylindrical shells with poroelastic core and external mean flow. Composite Structures, 135, 383–396 (2016) |
| [21] | TALEBITOOTI, R., DANESHJOU, K., and KORNOKAR, M. Three dimensional sound transmission through poroelastic cylindrical shells in the presence of subsonic flow. Journal of Sound and Vibration, 363, 380–406 (2016) |
| [22] | MAGNIEZ, J., ALI HAMDI, M., CHAZOT, J. D., and TROCLET, B. A mixed “Biot-shell” analytical model for the prediction of sound transmission through a sandwich cylinder with a poroelastic core. Journal of Sound and Vibration, 360, 203–223 (2016) |
| [23] | GEYER, T. F. and SARRADJ, E. Circular cylinders with soft porous cover for flow noise reduction. Experiments in Fluids, 57, 30 (2016) |
| [24] | TALEBITOOTI, R., GOHARI, H. D., and ZARASTVAND, M. R. Multi objective optimization of sound transmission across laminated composite cylindrical shell lined with porous core investigating non-dominated sorting genetic algorithm. Aerospace Science and Technology, 69, 269–280 (2017) |
| [25] | DANESHJOU, K., TALEBITOOTI, R., and KORNOKAR, M. Vibroacoustic study on a multilayered functionally graded cylindrical shell with poroelastic core and bonded-unbonded configuration. Journal of Sound and Vibration, 393, 157–175 (2017) |
| [26] | OLIAZADEH, P., FARSHIDIANFAR, A., and CROCKER, M. J. Experimental and analytical investigation on sound transmission loss of cylindrical shells with absorbing material. Journal of Sound and Vibration, 434, 28–43 (2018) |
| [27] | TALEBITOOTI, R., CHOUDARI KHAMENEH, A. M., ZARASTVAND, M. R., and KORNOKAR, M. Investigation of three-dimensional theory on sound transmission through compressed poroelastic sandwich cylindrical shell in various boundary configurations. Journal of Sandwich Structures & Materials, 21, 2313–2357 (2019) |
| [28] | GOLZARI, M. and JAFARI, A. A. Sound transmission loss through triple-walled cylindrical shells with porous layers. The Journal of the Acoustical Society of America, 143, 3529–3544 (2018) |
| [29] | DARVISH GOHARI, H., ZARASTVAND, M., and TALEBITOOTI, R. Acoustic performance prediction of a multilayered finite cylinder equipped with porous foam media. Journal of Vibration and Control, 26, 899–912 (2020) |
| [30] | ZHANG, Q. L. Sound transmission through micro-perforated double-walled cylindrical shells lined with porous material. Journal of Sound and Vibration, 485, 115539 (2020) |
| [31] | SHAHSAVARI, H., TALEBITOOTI, R., and KORNOKAR, M. Analysis of wave propagation through functionally graded porous cylindrical structures considering the transfer matrix method. Thin-Walled Structures, 159, 107212 (2021) |
| [32] | SHAHSAVARI, H., KORNOKAR, M., TALEBITOOTI, R., and DANESHJOU, K. The study of sound transmission through sandwich cylindrical shells with circumferentially corrugated cores filled with porous materials. Composite Structures, 291, 115608 (2022) |
| [33] | THONGCHOM, C., JEARSIRIPONGKUL, T., REFAHATI, N., ROUDGAR SAFFARI, P., ROODGAR SAFFARI, P., SIRIMONTREE, S., and KEAWSAWASVONG, S. Sound transmission loss of a honeycomb sandwich cylindrical shell with functionally graded porous layers. Buildings, 12, 151 (2022) |
| [34] | TALEBITOOTI, R. and ZARASTVAND, M. R. The effect of nature of porous material on diffuse field acoustic transmission of the sandwich aerospace composite doubly curved shell. Aerospace Science and Technology, 78, 157–170 (2018) |
| [35] | TALEBITOOTI, R., ZARASTVAND, M. R., and GOHARI, H. D. The influence of boundaries on sound insulation of the multilayered aerospace poroelastic composite structure. Aerospace Science and Technology, 80, 452–471 (2018) |
| [36] | TALEBITOOTI, R., ZARASTVAND, M., and DARVISHGOHARI, H. Multi-objective optimization approach on diffuse sound transmission through poroelastic composite sandwich structure. Journal of Sandwich Structures & Materials, 23, 1221–1252 (2021) |
| [37] | ZARASTVAND, M. R., ASADIJAFARI, M. H., and TALEBITOOTI, R. Improvement of the low-frequency sound insulation of the poroelastic aerospace constructions considering Pasternak elastic foundation. Aerospace Science and Technology, 112, 106620 (2021) |
| [38] | WANG, Y. D., LIAN, Y. P., WANG, Z. D., WANG, C. P., and FANG, D. N. A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties. Applied Mathematics and Mechanics (English Edition), 45(2), 217–238 (2024) https://doi.org/10.1007/s10483-024-3079-7 |
| [39] | AL-KETAN, O. and ABU AL-RUB, R. K. Multifunctional mechanical metamaterials based on triply periodic minimal surface lattices. Advanced Engineering Materials, 21, 1900524 (2019) |
| [40] | CAI, Z. Z., LIU, Z. H., HU, X. D., KUANG, H. K., and ZHAI, J. S. The effect of porosity on the mechanical properties of 3D-printed triply periodic minimal surface (TPMS) bioscaffold. Bio-Design and Manufacturing, 2, 242–255 (2019) |
| [41] | VIET, N. V. and ZAKI, W. Free vibration and buckling characteristics of functionally graded beams with triply periodic minimal surface architecture. Composite Structures, 274, 114342 (2021) |
| [42] | SIMSEK, U., ARSLAN, T., KAVAS, B., GAYIR, C. E., and SENDUR, P. Parametric studies on vibration characteristics of triply periodic minimum surface sandwich lattice structures. The International Journal of Advanced Manufacturing Technology, 115, 675–690 (2021) |
| [43] | LI, Z. T., CHEN, Z. B., CHEN, X. B., and ZHAO, R. C. Mechanical properties of triply periodic minimal surface (TPMS) scaffolds: considering the influence of spatial angle and surface curvature. Biomechanics and Modeling in Mechanobiology, 22, 541–560 (2023) |
| [44] | ZHANG, Y. J., LIU, B., PENG, F., JIA, H. R., ZHAO, Z. A., DUAN, S. Y., WANG, P. D., and LEI, H. S. Adaptive enhancement design of triply periodic minimal surface lattice structure based on non-uniform stress distribution. Applied Mathematics and Mechanics (English Edition), 44(8), 1317–1330 (2023) https://doi.org/10.1007/s10483-023-3013-9 |
| [45] | FENG, G. Z., LI, S., XIAO, L. J., and SONG, W. D. Mechanical properties and deformation behavior of functionally graded TPMS structures under static and dynamic loading. International Journal of Impact Engineering, 176, 104554 (2023) |
| [46] | ZHAO, M., LI, X. W., ZHANG, D. Z., and ZHAI, W. TPMS-based interpenetrating lattice structures: design, mechanical properties and multiscale optimization. International Journal of Mechanical Sciences, 244, 108092 (2023) |
| [47] | STEPINAC, L., GALI?, J., and BINI?KI, M. Fast estimation of bending stiffness in sandwich-structured composites with 3D printed TPMS core. Mechanics of Advanced Materials and Structures, 31, 9200–9209 (2024) |
| [48] | PHUNG-VAN, P., HUNG, P. T., NGUYEN-GIA, H., and NGUYEN-XUAN, H. Free vibration analysis of functionally graded triply periodic minimal surface plates using a first order shear deformation theory and meshfree method. Journal of Advanced Engineering and Computation, 7, 237–246 (2023) |
| [49] | NGUYEN-XUAN, H., TRAN, K. Q., THAI, C. H., and LEE, J. Modelling of functionally graded triply periodic minimal surface (FG-TPMS) plates. Composite Structures, 315, 116981 (2023) |
| [50] | BOROVKOV, A. I., MASLOV, L. B., ZHMAYLO, M. A., TARASENKO, F. D., and NEZHINSKAYA, L. S. Finite element analysis of elastic properties of metamaterials based on triply periodic minimal surfaces. Materials Physics and Mechanics, 52, 11–29 (2024) |
| [51] | NGUYEN, N. V. Free vibration analysis of functionally graded triply periodic minimal surface plates. Proceedings of the International Conference on Sustainable Energy Technologies, Springer, Singapore, 319–328 (2024) |
| [52] | LUO, T. H., WANG, L. Z., LIU, F. Y., CHEN, M., and LI, J. Modal response improvement of periodic lattice materials with a shear modulus-based FE homogenized model. Materials, 17, 1314 (2024) |
| [53] | ABUEIDDA, D. W., JASIUK, I., and SOBH, N. A. Acoustic band gaps and elastic stiffness of PMMA cellular solids based on triply periodic minimal surfaces. Materials & Design, 145, 20–27 (2018) |
| [54] | VIET, N. V., KARATHANASOPOULOS, N., and ZAKI, W. Mechanical attributes and wave propagation characteristics of TPMS lattice structures. Mechanics of Materials, 172, 104363 (2022) |
| [55] | ZHANG, P. F., LI, Z. H., LIU, B., ZHOU, Y. J., ZHAO, M., SUN, G. H., PEI, S. C., KONG, X. N., and BAI, P. K. Sound absorption performance of micro-perforated plate sandwich structure based on triply periodic minimal surface. Journal of Materials Research and Technology, 27, 386–400 (2023) |
| [56] | LIN, C. G., WEN, G. L., YIN, H. F., WANG, Z. P., LIU, J., and XIE, Y. M. Revealing the sound insulation capacities of TPMS sandwich panels. Journal of Sound and Vibration, 540, 117303 (2022) |
| [57] | WU, Y. Z., QI, X., SUN, L. F., WANG, B., HU, L., WANG, P., and LI, W. J. Sound transmission loss and bending properties of sandwich structures based on triply periodic minimal surfaces. Thin-Walled Structures, 204, 112324 (2024) |
| [58] | ZHANG, L., FEIH, S., DAYNES, S., CHANG, S., WANG, M. Y., WEI, J., and LU, W. F. Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading. Additive Manufacturing, 23, 505–515 (2018) |
| [59] | WANG, H. D., LI, S. Q., and WANG, C. X. Energy absorption characteristics of triply periodic minimal surface lattices. Journal of Physics: Conference Series, 2535, 012025 (2023) |
| [60] | QIU, N., WAN, Y. H., SHEN, Y. J., and FANG, J. G. Experimental and numerical studies on mechanical properties of TPMS structures. International Journal of Mechanical Sciences, 261, 108657 (2024) |
| [61] | ZARASTVAND, M. R., GHASSABI, M., and TALEBITOOTI, R. Acoustic insulation characteristics of shell structures: a review. Archives of Computational Methods in Engineering, 28, 505–523 (2021) |
| [62] | RAJAGOPALAN, S. and ROBB, R. A. Schwarz meets Schwann: design and fabrication of biomorphic and durataxic tissue engineering scaffolds. Medical Image Analysis, 10, 693–712 (2006) |
| [63] | ALMAHRI, S., SANTIAGO, R., LEE, D. W., RAMOS, H., ALABDOULI, H., ALTENEIJI, M., GUAN, Z. W., CANTWELL, W., and ALVES, M. Evaluation of the dynamic response of triply periodic minimal surfaces subjected to high strain-rate compression. Additive Manufacturing, 46, 102220 (2021) |
| [64] | QATU, M. S. Vibration of Laminated Shells and Plates, Elsevier, Amsterdam (2004) |
| [65] | BLAISE, A. and LESUEUR, C. Acoustic transmission through a 2-D orthotropic multi-layered infinite cylindrical shell. Journal of Sound and Vibration, 155, 95–109 (1992) |
| [66] | KOVAL, L. R. On sound transmission into a thin cylindrical shell under “flight conditions”. Journal of Sound and Vibration, 48, 265–275 (1976) |
| [67] | REAEI, S., TARKASHVAND, A., and TALEBITOOTI, R. Applying a functionally graded viscoelastic model on acoustic wave transmission through the polymeric foam cylindrical shell. Composite Structures, 244, 112261 (2020) |
| [68] | LEE, J. H. and KIM, J. Study on sound transmission characteristics of a cylindrical shell using analytical and experimental models. Applied Acoustics, 64, 611–632 (2003) |
| [69] | WANG, W. C., QATU, M. S., and YARAHMADIAN, S. Accuracy of shell and solid elements in vibration analyses of thin- and thick-walled isotropic cylinders. International Journal of Vehicle Noise and Vibration, 8, 221–236 (2012) |
| [70] | BLEVINS, R. D. Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York (1979) |
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