Abstract
The transmission properties of elastic waves propagating in a three-dimensional composite structure embedded periodically with spherical inclusions are analyzed by the transfer matrix method in this paper. Firstly, the periodic composite structures are divided into many layers, the transfer matrix of monolayer structure is deduced by the wave equations, and the transfer matrix of the entire structure is obtained in the case of boundary conditions of displacement and stress continuity between layers. Then, the effective impedance of the structure is analyzed to calculate its reflectivity and transmissivity of vibration isolation. Finally, numerical simulation is carried out; the experiment results validate the accuracy and feasibility of the method adopted in the paper and some useful conclusions are obtained.
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References
Chen Y.-Y. and Ye Z. (2001). Phys. Rev. E 64: 036616
Psarobas I.E., Stefanou N. and Modinos A. (2000). Phys. Rev. B 62: 278
Esquivel-Sirvent R. and Cocoletzi G.H. (1994). Band structure for the propagation of elastic waves in superlattices. J. Acoust. Soc. Am. 95(1): 86–90
Achenbach J.D. and Kitahara M. (1987). Harmonic waves in a solid with a periodic distribution of spherical cavities. J. Acoust. Soc. Am. 81(3): 595–598
Angel Y.C. and Achenbach J.D. (1987). Harmonic waves in an elastic solid containing a doubly periodic array of cracks. Wave Motion 9: 377–385
Achenbach J.D. and Kitahara M. (1986). Refection and transmission of an obliquely incident wave by an array of spherical cavities. J. Acoust. Soc. Am. 80(4): 1209–1214
Achenbach J.D. and Li Z.L. (1986). Propagation of horizontally polarized transverse waves in a solid with a periodic distribution of cracks. Wave Motion 8: 371–379
Angel Y.C. and Achenbach J.D. (1985). Reflection and transmission of elastic waves by a periodic array of cracks. J. Appl. Mech. 52: 33–41
Hemond C.J. (1983). Engineering acoustics and noise control [M]. Prentice-Hall, Englewood Cliffs
Eisley J. (1989). Mechanics of elastic structures: classical and finite element methods[M]. Prentice Hall, Englewood Cliffs
Halevi P. and Fuchs R. (1984). Generalised additional boundary condition for non-local dielectrics: I. Reflectivity. J. Phys. C Solid State Phys. 17: 3869–3888
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Project (No. 50075029) supported by the National Natural Science Foundation of China.
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Yong, W., Qibai, H., Minggang, Z. et al. Transfer matrix approach of vibration isolation analysis of periodic composite structure. Arch Appl Mech 77, 461–471 (2007). https://doi.org/10.1007/s00419-006-0106-9
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DOI: https://doi.org/10.1007/s00419-006-0106-9