ELASTIC WAVE BAND GAPS IN A TWO-DIMENSIONAL MAGNETOELECTROELASTIC PHONONIC CRYSTAL
DOI:
https://doi.org/10.26512/ripe.v2i13.21632Palavras-chave:
Magnetoelectroelastic phononic crystal. In-plane wave propagation. Full band gaps. Vibration control. Plane wave expansion method.Resumo
In this study we investigated the band structure of elastic waves propagating in a magnetoelectroelastic phononic crystal (MPC), consisting of a polymer matrix reinforced by BaTiO3”“CoFe2O4 inclusions in a square, triangular and honeycomb lattices. We also studied the influence of the inclusion geometry cross section ”“ circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to the x, y axes. The plane wave expansion (PWE) method was used to solve the constitutive equations of a magnetoelectroelastic material considering the wave propagation in the xy plane (longitudinal-transverse vibration, XY mode, and transverse vibration, Z mode). The complete band gaps between the XY and Z modes were observed to all types of inclusion and the best performance depends on the lattice. For square lattice, the best performance was found for square inclusion in lower frequencies, for triangular lattice, the circular, square and rotated square present, approximately, the same behavior and for honeycomb lattice, the best performance was found for circular inclusion.
Downloads
Referências
Anjos, V. & Arantes, A., 2015. Phononic band structure in carbon microtube composites. RSC Advances, Vol. 5, pp. 11248”“11253.
Benchabane, S., Khelif, A., Robert, L., Rauch, J.Y., Pastureaud, T. & Laude, V. 2006. Elastic band gaps for surface modes in an ultrasonic lithium niobate phononic crystal, Proceedings SPIE, vol. 6182, n. 618216, pp. 1”“13.
Bloch, F., 1928. Über die Quantenmechanik der Electron in Kristallgittern. Zeitschrift für Physik, vol. 52, pp. 550”“600.
Bou Matar, O., Robillard, J.F., Vasseur, J.O., Hladky-Hennion, A.-C. & Deymier P.A., 2012.
Band gap tunability of magneto-elastic phononic crystal. Journal of Applied Physics, vol. 111, n. 054901, pp. 1”“15.
Casadei, F., Dozio, L., Ruzzene, M. & Cunefare, K.A., 2010. Periodic shunts arrays for the control of noise radiation in an enclosure. Journal of Sound and Vibration, vol. 329, pp. 3632”“3646.
Casadei, F., Beck, B.S., Cunefare, K.A. & Ruzzene, M., 2012. Vibration control of plates through hybrid configurations of periodic piezoeletric shunts. Journal of Intelligent Material Systems and Structures, vol. 23, n. 10, pp. 1169”“1177.
Cassagne, D., Jouanin, C., Bertho, D., 1996. Hexagonal photonic-band gap structures. Physical Review B, vol. 53, n. 11, pp. 7134”“7142.
Dyogtyev, A.V., Sukhoivanov, I.A., De La Rue, R.M., 2010. Photonic band-gaps maps for different two dimensionally periodic photonic crystal structures. Journal of Applied Physics, vol. 107, n. 013108, pp. 1”“7.
Floquet, G., 1883. Sur les équations différentielles linéaires à coefficients périodiques. Annales scientifiques de l'École Normale Supérieure, vol. 12, pp. 47”“88.
Gao, Z., Fang, J., Zhang, Y., Jiang, L., 2013. Band structure research of a 2D honeycomb lattice phononic crystal. International Journal of Electrochemical Science, vol. 8, pp. 7918”“7925.
Ho, K.M., Cheng, C.K., Yang, Z., Zhang, X.X. & Sheng, P., 2003. Broadband locally resonant sonic shields. Applied Physics Letters, vol. 83, n. 26, pp. 5566”“5568.
Hou, Z., Wu, F. & Liu, Y., 2004. Phononic crystals containing piezoelectric material. . Solid State Communications, vol. 130, pp. 745”“749.
Huang, J. & Shi, Z., 2013. Attenuation zones of periodic pile barriers and its application in vibration reduction for plane waves. Journal of Sound and Vibration, vol. 332, pp. 4423”“ 4439.
Jensen, J.S., 2003. Phononic band gaps and vibrations in one- and two-dimensional massspring structures. Journal of Sound and Vibration, vol. 266, pp. 1053”“1078.
Kushwaha, M.S., Halevi, P. & Martínez, G., 1994, Theory of acoustic band structure of periodic elastic composites, Physical Review B, vol. 49, pp. 2313”“2322.
Lian, Z., Jiang, S., Hu, H., Dai, L., Chen, X. & Jiang, W., 2016. An enhanced plane wave expansion method to solve piezoelectric phononic crystal with resonant shunting circuits. Shock and Vibration, vol. 2016, n. 4015363, pp. 1”“13.
Miranda Jr., E.J.P. & Dos Santos, J.M.C., 2015. Flexural wave band gaps in metamaterial elastic beam, Proceedings of the 23rd ABCM International Congress of Mechanical Engineering, Rio de Janeiro, Brazil, pp. 1”“8.
Miranda Jr., E.J.P. & Dos Santos, J.M.C., 2016a. Phononic band gaps in Al2O3/epoxy composite, Submitted to Materials Science Forum, pp. 1”“10.
Miranda Jr., E.J.P. & Dos Santos, J.M.C., 2016b. Flexural wave band gaps in elastic metamaterial thin plate, Proceedings of the IX Mechanical Engineering Brazilian Congress, Fortaleza, Brazil, pp. 1”“10.
Miranda Jr., E.J.P. & Dos Santos, J.M.C., 2016c. Flexural wave band gaps in Al2O3/epoxy composite rectangular plate using Mindlin theory, Proceedings of the 3rd Brazilian Conference on Composite Materials, Gramado, Brazil, pp. 1”“8.
Olsson III, R.H. & El-Kady, I., 2009. Microfabricated phononic crystal devices and applications, Measurement Science and Technology, vol. 20, n. 012002, pp. 1”“13.
Pennec, Y., Vasseur, J.O., Djafari-Rouhani, B., DobrzyÅ„ski, L. & Deymier, P.A., 2010. Twodimensional phononic crystals: Examples and applications. Surface Science Reports, vol. 65, pp. 229”“291.
Qiu, C.Y., Liu, Z.Y., Mei, J. & Shi, J., 2005. Mode-selecting acoustic filter by using resonant tunneling of two-dimensional double phononic crystals, Applied Physics Letters, vol. 87, n. 104101, pp. 1”“3.
Robillard, J.-F., Bou Matar, O., J.F., Vasseur, J.O., Deymier P.A., Stippinger, M., Hladky- Hennion, A.-C, Pennec, Y. & Djafari-Rouhani, B., 2009. Tunable magnetoelastic phononic crystals. Applied Physics Letters, vol. 95, n. 124104, pp. 1”“4.
Sigalas, M.M. & Economou, E.N., 1994. Elastic waves in plates with periodically placed inclusions. Journal of Applied Physics, vol. 75, pp. 2845”“2850.
Vasseur, J.O., Bou Matar, O., J.F., Robillard, J.-F., Hladky-Hennion, A.-C & Deymier P.A., 2011. Band structures tunability of bulk 2D phononic crystals made of magneto-elastic materials. AIP Advances, vol. 1, n. 041904, pp. 1”“13.
Wang, G., Wen, J.H. & Wen, X.S., 2005. Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method: application to locally resonant beams with flexural wave band gap, Physical Review B, vol. 71, n. 104302, pp. 1”“5.
Wang, X.-M. & Shen, Y.-P., 1996. The conservations laws and path-independent integrals with an application for linear electro-magneto-elastic media, International Journal of Solids and Structures, vol. 33, n. 6, pp. 865”“878.
Wang, Y.-Z., Li, F.-M., Huang, W.-H., Jiang, X., Wang, Y.-S. & Kishimoto, K., 2008. Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals, International Journal of Solids and Structures, vol. 48, pp. 4203”“4210.
Wang, Y.-Z., Li, F.-M., Kishimoto, K., Wang, Y.-S. & Huang, W.-H., 2009. Elastic wave band gaps in magnetoelectroelastic phononic crystals, Wave Motion, vol. 46, pp. 47”“56.
Wilm, M., Ballandras, S., Laude, V. & Pastureaud, T., 2001. A plane-wave-expansion approach for modelling acoustic propagation in 2D and 3D piezoelectric periodic structures. IEEE Ultrasonics Symposium, vol. 2, pp. 977”“980.
Wilm, M., Ballandras, S., Laude, V. & Pastureaud, T., 2002. A full 3D plane-wave-expansion model for 1-3 piezoelectric composite structures. Journal of the Acoustical Society of America, vol. 112, n. 3, pp. 943”“952.
Wilm, M., Khelif, A., Ballandras, S. & Laude, V., 2003. Out-of-plane propagation of elastic waves in two-dimensional phononic band-gap materials. Physical Review E, vol. 67, n. 065602, pp. 1”“4.
Xiao, Y., Wen, J. & Wen, X., 2012. Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators. Journal of Sound and Vibration, vol. 331, pp. 5408”“5423.
Yang, Z., Dai, H.M., Chan, N.H. & Ma, G.C., 2003. Acoustic metamaterial panels for sound attenuation in the 50”“1000 Hz regime. Applied Physics Letters, vol. 96, n. 041906, pp. 1”“3.
Yu, K., Chen, T. & Wang, X., 2013. Band gaps in the low-frequency range based on the twodimensional phononic crystals plates composed of rubber matrix with periodic steel stubs. Physica B, vol. 416, pp. 12”“16.
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Autores que publicam nesta revista concordam com os seguintes termos:
Autores mantém os direitos autorais e concedem à revista o direito de primeira publicação, sendo o trabalho simultaneamente licenciado sob a Creative Commons Attribution License o que permite o compartilhamento do trabalho com reconhecimento da autoria do trabalho e publicação inicial nesta revista.
Autores têm autorização para assumir contratos adicionais separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
Autores têm permissão e são estimulados a publicar e distribuir seu trabalho online (ex: em repositórios institucionais ou na sua página pessoal) a qualquer ponto antes ou durante o processo editorial, já que isso pode gerar alterações produtivas, bem como aumentar o impacto e a citação do trabalho publicado.
