Dispersion equation of Rayleigh waves in transversely isotropic nonlocal piezoelastic solids half-space
Keywords:dispersion equation, nonlocal, piezoelastic
This study is devoted to investigate the propagation of Rayleigh-type waves in transversely isotropic nonlocal piezoelastic half-space. When the stress-free boundary is maintained at charge-free condition, the dispersion equation for the propagation of Rayleigh waves at the free surface of transversely isotropic piezoelastic solids has been obtained. Based on the obtained dispersion equation, the effect of the nonlocality on the speed of Rayleigh wave is numerically considered. The dependence of velocities of plane waves in transversely isotropic nonlocal piezoelastic medium on the direction of propagation as well as non-dimensional frequency parameter has been also illustrated.
J. N. Sharma, M. Pal, and D. Chand. Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials. Journal of Sound and Vibration, 284, (1-2), (2005), pp. 227–248. https://doi.org/10.1016/j.jsv.2004.06.036.
J. Yang. An introduction to the theory of piezoelectricity. Springer, (2005).
L. P. Zinchuk and A. N. Podlipenets. Dispersion equations for Rayleigh waves in a piezoelectric
periodically layered structure. Journal of Mathematical Sciences, 103, (3), (2001), pp. 398–403. https://doi.org/10.1023/A:1011382816558.
A. K. Vashishth and V. Gupta. Wave propagation in transversely isotropic porous piezoelectric materials. International Journal of Solids and Structures, 46, (20), (2009), pp. 3620–3632. https://doi.org/10.1016/j.ijsolstr.2009.06.011.
G. Z. Voyiadjis. Handbook of nonlocal continuum mechanics for materials and structures. Springer Nature Switzerland AG, (2018).
A. C. Eringen and D. G. B. Edelen. On nonlocal elasticity. International Journal of Engineering Science, 10, (3), (1972), pp. 233–248. https://doi.org/10.1016/0020-7225(72)90039-0.
L.-L. Ke and Y.-S. Wang. Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Materials and Structures, 21, (2), (2012). https://doi.org/10.1088/0964-1726/21/2/025018.
L.-L. Ke, Y.-S. Wang, and Z.-D. Wang. Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory. Composite Structures, 94, (6), (2012), pp. 2038–2047. https://doi.org/10.1016/j.compstruct.2012.01.023.
L.-H. Ma, L.-L. Ke, Y.-Z. Wang, and Y.-S. Wang. Wave propagation analysis of piezoelectric nanoplates based on the nonlocal theory. International Journal of Structural Stability and Dynamics, 18, (04), (2018) . https://doi.org/10.1142/S0219455418500608.
A.-L. Chen, D.-J. Yan, Y.-S. Wang, and C. Zhang. Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures. Ultrasonics, 65, (2016), pp. 154–164. https://doi.org/10.1016/j.ultras.2015.10.006.
D.-J. Yan, A.-L. Chen, Y.-S. Wang, C. Zhang, and M. Golub. Propagation of guided elastic waves in nanoscale layered periodic piezoelectric composites. European Journal of Mechanics-A/Solids, 66, (2017), pp. 158–167. https://doi.org/10.1016/j.euromechsol.2017.07.003.
D.-J. Yan, A.-L. Chen, Y.-S. Wang, C. Zhang, and M. Golub. In-plane elastic wave propagation in nanoscale periodic layered piezoelectric structures. International Journal of Mechanical Sciences, 142, (2018), pp. 276–288. https://doi.org/10.1016/j.ijmecsci.2018.04.054.
F.-M. Li and Y.-S. Wang. Study on localization of plane elastic waves in disordered periodic 2–2 piezoelectric composite structures. Journal of Sound and Vibration, 296, (3), (2006), pp. 554–566. https://doi.org/10.1016/j.jsv.2006.01.057.
J. N. Sharma and V. Walia. Further investigations on Rayleigh waves in piezothermoelastic materials. Journal of Sound and Vibration, 301, (1-2), (2007), pp. 189–206. https://doi.org/10.1016/j.jsv.2006.09.018.
A. C. Eringen. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54, (9), (1983), pp. 4703–4710. https://doi.org/10.1063/1.332803.
P. C. Vinh, V. T. N. Anh, D. X. Tung, and N. T. Kieu. Homogenization of very rough interfaces for the micropolar elasticity theory. Applied Mathematical Modelling, 54, (2018), pp. 467–482. https://doi.org/10.1016/j.apm.2017.09.039.