Guided wave propagation in rotating functionally graded annular plates. (English) Zbl 1383.74059
Summary: Elastic guided wave propagation in a rotating functionally graded material (FGM) annular plate is presented in this paper. The material properties are assumed to vary continuously along the radial direction. The elastodynamic equation of annular plates which take into account initial hoop, centrifugal and Coriolis effects is derived, and the wave finite element method is extended to model wave motion related to rotation with 3D-Chebyshev spectral elements. Firstly, wave properties in a straight bar are computed and compared to that of the Rayleigh-Ritz method. Then, wave propagation in the FGM annular plate with various material gradient indexes is considered and the results indicate that the index has large influence on wave characteristics. With contour profiles of transverse sections, propagating wave modes in the plate can be identified distinctly. Besides, the effects of rotation on wave propagation are discussed, which show that the extensional-like and shearing-like wave modes are very sensitive to the rotation at low frequencies but the flexural are not. In addition, the curve veering phenomenon existing in FGM annular plates is also found, which analyzes the influences of material gradient index and rotating speed and points out the variations in the relative critical frequencies.
MSC:
| 74K20 | Plates |
| 74A40 | Random materials and composite materials |
| 74J99 | Waves in solid mechanics |
| 74S25 | Spectral and related methods applied to problems in solid mechanics |
References:
| [1] | Yamanouchi, M., Koizumi, M.: Functionally gradient materials. In: Proceeding of the first international symposium on functionally graded materials (1991) |
| [2] | Liu, G., Tani, J., Ohyoshi, T.: Lamb waves in a functionally gradient material plates and its transient response. Part 1: theory; part 2: calculation results. Trans. Jpn. Soc. Mech. Eng. 57(535), 603-611 (1991) · doi:10.1299/kikaia.57.603 |
| [3] | Han, X., Liu, G., Xi, Z., Lam, K.: Transient waves in a functionally graded cylinder. Int. J. Solids Struct. 38(17), 3021-3037 (2001) · Zbl 0977.74035 · doi:10.1016/S0020-7683(00)00219-5 |
| [4] | Chakraborty, A., Gopalakrishnan, S.: A spectrally formulated finite element for wave propagation analysis in functionally graded beams. Int. J. Solids Struct. 40(10), 2421-2448 (2003) · Zbl 1087.74636 · doi:10.1016/S0020-7683(03)00029-5 |
| [5] | Berezovski, A., Engelbrecht, J., Maugin, G.A.: Numerical simulation of two-dimensional wave propagation in functionally graded materials. Eur. J. Mech. A Solids 22(2), 257-265 (2003) · Zbl 1038.74575 · doi:10.1016/S0997-7538(03)00029-9 |
| [6] | Elmaimouni, L., Lefebvre, J., Zhang, V., Gryba, T.: Guided waves in radially graded cylinders: a polynomial approach. Ndt & E Int. 38(5), 344-353 (2005) · Zbl 1189.74057 · doi:10.1016/j.ndteint.2004.10.004 |
| [7] | Shakeri, M., Akhlaghi, M., Hoseini, S.: Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder. Compos. Struct. 76(1), 174-181 (2006) · doi:10.1016/j.compstruct.2006.06.022 |
| [8] | Chen, W., Wang, H., Bao, R.: On calculating dispersion curves of waves in a functionally graded elastic plate. Compos. Struct. 81(2), 233-242 (2007) · doi:10.1016/j.compstruct.2006.08.009 |
| [9] | Yu, J.G., Wu, B., He, C.F.: Characteristics of guided waves in graded spherical curved plates. Int. J. Solids Struct. 44(11), 3627-3637 (2007) · Zbl 1137.74029 |
| [10] | Sun, D., Luo, S.-N.: Wave propagation of functionally graded material plates in thermal environments. Ultrasonics 51(8), 940-952 (2011) · doi:10.1016/j.ultras.2011.05.009 |
| [11] | Cao, X., Jin, F., Jeon, I.: Calculation of propagation properties of lamb waves in a functionally graded material (fgm) plate by power series technique. NDT & E Int. 44(1), 84-92 (2011) · doi:10.1016/j.ndteint.2010.09.010 |
| [12] | Mehrkash, M., Azhari, M., Mirdamadi, H.R.: Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates. Ultrasonics 54(1), 106-120 (2014) · doi:10.1016/j.ultras.2013.04.022 |
| [13] | Yu, J., Yang, X., Lefebvre, J., Zhang, C.: Wave propagation in graded rings with rectangular cross-sections. Wave Motion 52, 160-170 (2015) · Zbl 1454.74066 · doi:10.1016/j.wavemoti.2014.09.009 |
| [14] | Mace, B.R., Duhamel, D., Brennan, M.J., Hinke, L.: Finite element prediction of wave motion in structural waveguides. J. Acoust. Soc. Am. 117(5), 2835-2843 (2005) · doi:10.1121/1.1887126 |
| [15] | Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Courier Corporation, Chelmsford (2001) · Zbl 0994.65128 |
| [16] | Pozrikidis, C.: Introduction to Finite and Spectral Element Methods using MATLAB. CRC Press, Boca Raton (2005) · Zbl 1078.65109 |
| [17] | Auriault, J.-L.: Body wave propagation in rotating elastic media. Mech. Res. Commun. 31(1), 21-27 (2004) · Zbl 1072.74037 · doi:10.1016/j.mechrescom.2003.07.002 |
| [18] | Peng, X.-L., Li, X.-F.: Elastic analysis of rotating functionally graded polar orthotropic disks. Int. J. Mech. Sci. 60(1), 84-91 (2012) · doi:10.1016/j.ijmecsci.2012.04.014 |
| [19] | Nejad, M.Z., Rastgoo, A., Hadi, A.: Exact elasto-plastic analysis of rotating disks made of functionally graded materials. Int. J. Eng. Sci. 85, 47-57 (2014) · Zbl 1423.74156 · doi:10.1016/j.ijengsci.2014.07.009 |
| [20] | Li, C.L., Han, Q., Liu, Y.J., Liu, X.C., Wu, B.: Investigation of wave propagation in double cylindrical rods considering the effect of prestress. J. Sound Vib. 353, 164-180 (2015) · doi:10.1016/j.jsv.2015.05.017 |
| [21] | Mead, D.: Wave propagation in continuous periodic structures: research contributions from southampton, 1964-1995. J. Sound Vib. 190(3), 495-524 (1996) · doi:10.1006/jsvi.1996.0076 |
| [22] | Waki, Y., Mace, B., Brennan, M.: Free and forced vibrations of a tyre using a wave/finite element approach. J. Sound Vib. 323(3), 737-756 (2009) · doi:10.1016/j.jsv.2009.01.006 |
| [23] | Li, C.L., Han, Q., Liu, Y.J.: Thermoelastic wave characteristics in a hollow cylinder using the modified wave finite element method. Acta Mech. 227(6), 1711-1725 (2016) · Zbl 1341.74152 · doi:10.1007/s00707-016-1578-5 |
| [24] | Moser, F., Jacobs, L.J., Qu, J.: Modeling elastic wave propagation in waveguides with the finite element method. Ndt & E Int. 32(4), 225-234 (1999) · doi:10.1016/S0963-8695(98)00045-0 |
| [25] | Liu, Y.J., Han, Q., Huang, H.W., Li, C.L., Liu, X.C., Wu, B.: Computation of dispersion relations of functionally graded rectangular bars. Compos. Struct. 133, 31-38 (2015) · doi:10.1016/j.compstruct.2015.07.064 |
| [26] | Perkins, N., Mote, C.: Comments on curve veering in eigenvalue problems. J. Sound Vib. 106(3), 451-463 (1986) · doi:10.1016/0022-460X(86)90191-4 |
| [27] | Mace, B.R., Manconi, E.: Wave motion and dispersion phenomena: veering, locking and strong coupling effects. J. Acoust. Soc. Am. 131(2), 1015-1028 (2012) · doi:10.1121/1.3672647 |
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