Comparative study on vibro-acoustic properties of sandwich shells containing functionally-graded porous materials in a thermal environment

doi:10.1007/s10483-025-3251-6

Abstract

Abstract:

The dynamics of functionally-graded (FG) sandwich shells with varied pore distributions in thermal environments is investigated, focusing on their free vibration behaviors and sound transmission loss (STL) characteristics. The effective material parameters are calculated by integrating the graded distribution through three distinct pore distribution laws. The dynamic governing equations are derived by means of the first-order shear deformation theory, guided by Hamilton's principle. The solutions for the natural frequency and acoustic transmission loss factor are obtained from the shell's free vibration general solution and the acoustic displacement function, respectively. A detailed numerical analysis is conducted to assess the impacts of the structural and geometric parameters, as well as the ambient temperature, on the vibro-acoustic properties. The results indicate that vibro-acoustic coupling is most significant in shells with a symmetric non-uniform pore distribution, and the resonance frequency shifts towards lower frequencies as the power-law index increases. These findings offer valuable insights for enhancing the design of materials aimed at vibration damping and acoustic management.

Key words: functionally-graded (FG) porous material, cylindrical shell, thermal environment, sound transmission loss (STL), vibro-acoustic coupling

2010 MSC Number:

O327

Xinbiao XIAO, Xinte WANG, Jian HAN, Yuanpeng HE. Comparative study on vibro-acoustic properties of sandwich shells containing functionally-graded porous materials in a thermal environment. Applied Mathematics and Mechanics (English Edition), 2025, 46(5): 947-964.

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Figures/Tables 13

Fig. 1

Table 1

Material properties of the FG porous sandwich shell"

Material	$E$ /GPa	$ρ$ /(kg·m^-3)	$ν$	$ϑ$	$c 0$ /(m·s^-1)	$ρ 0$ /(kg·m^-3)	$P 0$ /Pa
Metal	70	2 700	0.3	$23 × 10 − 6$	–	–	–
Ceramic	380	3 800	0.3	$5.87 × 10 − 6$	–	–	–
Acoustic medium	–	–	–	–	340	1.293	1

Table 1

Table 2

Comparison of the natural frequency ω (Hz) of FG piezoelectric cylindrical shells"

$R / h$	Method	Circumferential wave number $n (m = 1)$
$R / h$	Method	1	5	10	20
50	Present	442.27	134.01	453.92	1 762.80
	Ref. [44]	464.02	130.46	437.73	1 799.81
	Ref. [49]	444.01	132.52	464.55	1 763.76
100	Present	442.19	87.79	228.80	900.98
	Ref. [44]	458.28	85.54	221.73	875.95
	Ref. [49]	442.34	85.88	238.57	915.39

Table 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Table 3

Variation of ω against γ and N for different types of FG shells"

Type	$N$	$γ$
Type	$N$	0.1	0.3	0.5	0.7	0.9
Type 1	0.05	2.651	2.582	2.517	2.458	2.451
	0.5	2.413	2.367	2.324	2.294	2.324
	5	2.135	2.120	2.114	2.132	2.230
Type 2	0.05	2.648	2.578	2.499	2.408	2.324
	0.5	2.408	2.348	2.280	2.203	2.139
	5	2.116	2.053	1.980	1.894	1.810
Type 3	0.05	2.635	2.536	2.417	2.261	2.014
	0.5	2.396	2.306	2.197	2.056	1.831
	5	2.109	2.030	1.934	1.810	1.612

Table 3

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

References 51

[1]	FEIZABAD, H. M. and YAS, M. H.Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fibers. Applied Mathematics and Mechanics (English Edition), 45(3), 543–562 (2024) https://doi.org/10.1007/s10483-024-3090-8
[2]	OCHÔA, P. A., GROVES, R. M., and BENEDICTUS, R.Effects of high-amplitude low-frequency structural vibrations and machinery sound waves on ultrasonic guided wave propagation for health monitoring of composite aircraft primary structures. Journal of Sound and Vibration, 475, 115289 (2020)
[3]	LIU, J. H., XUE, Y., GAO, Z. H., KRUSHYNSKA, A. O., and LI, J. Q.Actively tunable sandwich acoustic metamaterials with magnetorheological elastomers. Applied Mathematics and Mechanics (English Edition), 45(11), 1875–1894 (2024) https://doi.org/10.1007/s10483-024-3186-9
[4]	KARIM, M. A., JEON, Y., and KIM, D. B.Trailblazing multi-material structure: niobium alloy to tungsten-copper composite using wire-arc additive manufacturing. Materials Letters, 375, 137246 (2024)
[5]	ZHANG, J., YAO, D., SHEN, M. L., WANG, R. Q., LI, J., and GUO, S. Y.Effect of multi-layered IIR/EP on noise reduction of aluminium extrusions for high-speed trains. Composite Structures, 262, 113638 (2021)
[6]	ZHANG, Z. C., LI, H. Q., CHEN, J. H., and GONG, J. X.UIO-66-NH2/polydopamine double coating modification on cotton fabric for sound absorption and noise reduction. Materials Letters, 360, 135882 (2024)
[7]	JIANG, T. J., RØNNQUIST, A., SONG, Y., FRØSETH, G. T., and NÅVIK, P.A detailed investigation of uplift and damping of a railway catenary span in traffic using a vision-based line-tracking system. Journal of Sound and Vibration, 527, 116875 (2022)
[8]	HUANG, Q. Y., WANG, L., HUA, F. F., YOU, Q. Q., HE, W. K., ZHOU, H. H., GAO, J., WU, W. T., and ZHOU, X. Q.Random and harmonic responses of plain woven carbon fiber reinforced conical-conical shell based on machine learning multiscale modelling. Thin-Walled Structures, 203, 112220 (2024)
[9]	PENG, Y. H., ZHANG, D. C., SHENG, X. Z., and THOMPSON, D.A fundamental study on the performance of tuned mass dampers installed periodically on a fast-rotating train wheel. Journal of Sound and Vibration, 576, 118271 (2024)
[10]	ZHANG, J., YAO, D., PENG, W., WANG, R. Q., LI, J., and GUO, S. Y.Optimal design of lightweight acoustic metamaterials for low-frequency noise and vibration control of high-speed train composite floor. Applied Acoustics, 199, 109041 (2022)
[11]	WANG, X., DONG, K., and WANG, X. Y.Hygrothermal effect on dynamic interlaminar stresses in laminated plates with piezoelectric actuators. Composite Structures, 71, 220–228 (2005)
[12]	KOIZUMI, M.FGM activities in Japan. Composites Part B: Engineering, 28, 1–4 (1997)
[13]	RABIN, B. H. and SHIOTA, I.Functionally gradient materials. Materials Research Bulletin, 20, 14–18 (1995)
[14]	FANG, K., LI, N., LI, P., QIAN, Z. H., KOLESOV, V., and KUZNETSOVA, I.Effects of an attached functionally graded layer on the electromechanical behaviors of piezoelectric semiconductor fibers. Applied Mathematics and Mechanics (English Edition), 43(9), 1367–1380 (2022) https://doi.org/10.1007/s10483-022-2900-5
[15]	ZHOU, Y. Y., LIU, D. Y., HOU, D. G., LIU, J. H., LI, X. L., and YUE, Z. J.Wave propagation in the viscoelastic functionally graded cylindrical shell based on the first-order shear deformation theory. Materials, 16, 5914 (2023)
[16]	GAI, X. L., GUAN, X. W., CAI, Z. N., LI, X. H., HU, W. C., XING, T., and WANG, F.Acoustic properties of honeycomb like sandwich acoustic metamaterials. Applied Acoustics, 199, 109016 (2022)
[17]	STEPINAC, L., GALIĆ, J., and VASSILOPOULOS, A. P.Experimental and numerical investigation of an additively manufactured sandwich composite bridge deck utilizing gyroid building blocks. Composite Structures, 343, 118304 (2024)
[18]	ZENKERT, D.The Handbook of Sandwich Construction, EMAS Publishing, Warrington (1997)
[19]	PANDEY, A. M. and GOPAL, K. V. N.Transient vibration and sound radiation analysis of simply supported functionally graded sandwich plates. Composite Structures, 290, 115520 (2022)
[20]	PHAM, Q. H., HOANG, N. T., TRAN, T. T., and ZENKOUR, A. M.Random vibration analysis of functionally graded sandwich plates with different skin layers subjected to double explosive load: mathematical model with numerical solution proposition. Archives of Civil and Mechanical Engineering, 24, 220 (2024)
[21]	TUNG, H. V. and TRANG, L. T. N.Nonlinear stability of advanced sandwich cylindrical shells comprising porous functionally graded material and carbon nanotube reinforced composite layers under elevated temperature. Applied Mathematics and Mechanics (English Edition), 42(9), 1327–1348 (2021) https://doi.org/10.1007/s10483-021-2771-6
[22]	ASLAN, T. A., NOORI, A. R., and TEMEL, B.An efficient approach for free vibration analysis of functionally graded sandwich beams of variable cross-section. Structures, 58, 105397 (2023)
[23]	BAID, S., HILALI, Y., MESMOUDI, S., and BOURIHANE, O.Buckling analysis of functionally graded sandwich thin plates using a meshfree Hermite radial point interpolation method. Engineering with Computers, 41, 627–643 (2025)
[24]	SINGH, D., RAI, S., and GUPTA, A.Vibration analysis of sandwich functionally graded material plate with cut-outs using artificial neural network technique. Thin-Walled Structures, 202, 112072 (2024)
[25]	TAGHIPOUR, A. and DARDEL, M.Sound transmission loss in functionally graded porous metastructural plate with absorber. Journal of Vibration and Control, 30, 779–794 (2024)
[26]	CHEN, X. H., SHEN, H. S., and XIANG, Y.Thermo-mechanical postbuckling analysis of sandwich cylindrical shells with functionally graded auxetic GRMMC core surrounded by an elastic medium. Thin-Walled Structures, 171, 108755 (2022)
[27]	GARG, A., CHALAK, H. D., LI, L., BELARBI, M. O., SAHOO, R., and MUKHOPADYYAY, T.Vibration and buckling analyses of sandwich plates containing functionally graded metal foam core. Acta Mechanica Solida Sinica, 35, 1–16 (2022)
[28]	FOROUTAN, K. and DAI, L. M.Subharmonic and superharmonic resonances of five-layered porous functionally graded sandwich cylindrical shells with two-layered viscoelastic cores. Journal of Vibration and Control, 29, 4643–4658 (2023)
[29]	LIU, Y. F., QIN, Z. Y., and CHU, F. L.Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance. Applied Mathematics and Mechanics (English Edition), 42(6), 805–818 (2021) https://doi.org/10.1007/s10483-021-2740-7
[30]	LEI, C., QIAN, K., NOONAN, O., NOUWENS, A., and YU, C.Applications of nanomaterials in mass spectrometry analysis, Nanoscale, 5, 12033–12042 (2013)
[31]	KAREEM, A. S. and RESHAD, N. A.Influence of porosity on the free vibration response of sandwich functionally graded porous beams. Journal of Sustainable Construction Materials and Technologies, 7, 291–301 (2022)
[32]	XIE, K., CHEN, H. Y., WANG, Y. W., LI, J. C., and JIN, F.Nonlinear dynamic analysis of a geometrically imperfect sandwich beam with functionally graded material facets and auxetic honeycomb core in thermal environment. Aerospace Science and Technology, 144, 108794 (2024)
[33]	BAMDAD, M., MOHAMMADIMEHR, M., and ALAMBEIGI, K.Analysis of sandwich Timoshenko porous beam with temperature-dependent material properties: magneto-electro-elastic vibration and buckling solution. Journal of Vibration and Control, 25, 2875–2893 (2019)
[34]	QIN, B., MEI, J., and WANG, Q. S.Parametric analysis of free vibration of functionally graded porous sandwich rectangular plates resting on elastic foundation. Materials, 17, 2398 (2024)
[35]	NGUYEN, V. C., TRAN, H. Q., and TRAN, M. T.Nonlinear free vibration analysis of multi-directional functionally graded porous sandwich plates. Thin-Walled Structures, 203, 112204 (2024)
[36]	WATTANASAKULPONG, N., THAI, S., and EIADTRONG, S.Analyses on thermal vibration and stability of sandwich skew plates with functionally graded porous core. Structures, 58, 105536 (2023)
[37]	YUAN, W. H., LIAO, H. T., GAO, R. X., and LI, F. L.Vibration and sound transmission loss characteristics of porous foam functionally graded sandwich panels in thermal environment. Applied Mathematics and Mechanics (English Edition), 44(6), 897–916 (2023) https://doi.org/10.1007/s10483-023-3004-7
[38]	ZHANG, C. W., JIN, Q., SONG, Y. S., WANG, J. L., SUN, L., LIU, H. C., DUN, L. M., TAI, H., YUAN, X. D., XIAO, H. M., ZHU, L. M., and GUO, S. L.Vibration analysis of a sandwich cylindrical shell in hygrothermal environment. Nanotechnology Reviews, 10, 414–430 (2021)
[39]	YANG, S. F., MAHJOURI, H., and JAMALPOOR, A.Underwater temperature-dependent sound scattering and acoustic radiation force issues of a functionally graded sandwich spherical shell integrated with piezoelectric layers. Ocean Engineering, 294, 116730 (2024)
[40]	GAO, K., GAO, W., WU, B. H., WU, D., and SONG, C. M.Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales. Thin-Walled Structures, 125, 281–293 (2018)
[41]	ZHOU, Y. Y., ZHU, J., and LIU, D. Y.Dynamic analysis of laminated piezoelectric cylindrical shells. Engineering Structures, 209, 109945 (2020)
[42]	FAZZOLARI, F. A. and CARRERA, E.Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core. Journal of Sound and Vibration, 333, 1485–1508 (2014)
[43]	KHALILI, S. M. R., TAFAZOLI, S., and FARD, K. M.Free vibrations of laminated composite shells with uniformly distributed attached mass using higher order shell theory including stiffness effect. Journal of Sound and Vibration, 330, 6355–6371 (2011)
[44]	MEHRALIAN, F. and BENI, Y. T.Vibration analysis of size-dependent bimorph functionally graded piezoelectric cylindrical shell based on nonlocal strain gradient theory. Journal of The Brazilian Society of Mechanical Sciences and Engineering, 40, 27 (2018)
[45]	REAEI, S. H., 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)
[46]	SIRIMONTREE, S., THONGCHOM, C., SAFFARI, P. R., REFAHATI, N., SAFFARI, P. R., JEARSIRIPONGKUL, T., and KEAWSAWASVONG, S.Effects of thermal environment and external mean flow on sound transmission loss of sandwich functionally graded magneto-electro-elastic cylindrical nanoshell. European Journal of Mechanics A-Solids, 97, 104774 (2023)
[47]	ABDOLHOSEYNI, J. and DANESH, M.Sound transmission loss of a sandwich functionally graded cylindrical shell integrated with magneto-electro-elastic patches. Journal of Sound and Vibration, 543, 117350 (2023)
[48]	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)
[49]	SHENG, G. G. and WANG, X.Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells. Applied Mathematical Modelling, 34, 2630–2643 (2010)
[50]	NOURI, A. and ASTARAKI, S.Optimization of sound transmission loss through a thin functionally graded material cylindrical shell. Shock and Vibration, 2014, 814682 (2014)
[51]	ZHANG, X. M., LIU, G. R., and LAM, K. Y.Vibration analysis of thin cylindrical shells using wave propagation approach. Journal of Sound and Vibration, 239, 397–403 (2001)