Phase velocity of love waves as function of heterogeneity and void parameter

Yıl 2024, Cilt: 8 Sayı: 4, 603 - 610, 31.10.2024

Sandip Kumar Das , Anup Saha

https://doi.org/10.31127/tuje.1442355

Öz

The present study looks at the Love wave propagating through an elastic layer containing empty pores situated above a heterogeneous elastic semi-infinite space. We have constructed separate formulations of equations of motion for both media under congruous boundary conditions. The separation of variables approach is used to build the phase velocity frequency relation in compact form using the Whittaker function. The resulting closed-form dispersion equation matches the conventional Love wave equation when heterogeneity has been removed. The propagation of Love waves is strongly influenced by a porous layer of limited thickness across an elastic semi-infinite space. Three wave fronts are demonstrated to have the potential to propagate. The equilibrated inertia and the variation in the void volume fraction are related to two wave fronts that are connected to the characteristics of the void pores. Numerical treatments are applied and graphically illustrated to implement these effects associated to Love waves’ phase velocity.

Anahtar Kelimeler

Love waves, Wave front, Whittaker’s function, Void pores, Volume fraction

Teşekkür

The authors are grateful to VIT Chennai and Rampurhat College for providing all necessary facilities for research.

Kaynakça

• Ewing, W. M., Jardetzky, W. S., & Press, F. (1957). Elastic waves in layered media. McGraw-Hill Book Co.
• Love, A. E. H. (1944). A treatise on the mathematical theory of elasticity. Dover Publications.
• Achenbach, J. D. (1973). Wave propagation in elastic solids. North-Holland Publishing Company.
• Pilant, W. L. (1978). Elastic waves in the earth. Elsevier Scientific.
• Satô, Y. (1952). Study on surface waves, V: Love waves propagated upon heterogeneous medium. Bulletin of the Earthquake Research Institute, 30, 1-12.
• Satô, Y. (1952). Study on surface waves, VI: Generation of Love and other types of SH waves. Bulletin of the Earthquake Research Institute, 30, 101-120.
• Satô, Y. (1952). Study on surface waves, VII: Travel time of Love waves. Bulletin of the Earthquake Research Institute, 30, 305-317.
• Noyer, J. D. (1961). The effect of variations in layer thickness on Love waves. Bulletin of the Seismological Society of America, 51(2), 227-235.
• Biot, M. A. (1955). Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics, 26, 182-185.
• Biot, M. A. (1956). Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. Journal of the Acoustical Society of America, 28(2), 168-178.
• Biot, M. A. (1956). Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. Journal of the Acoustical Society of America, 28(2), 179-191.
• Nunziato, J. W., & Cowin, S. C. (1979). A non-linear theory of elastic material with voids. Archive for Rational Mechanics and Analysis, 72, 175-201.
• Chattopadhayay, A., Chakraborty, M., & Kushwaha, V. (1986). On the dispersion equation of Love waves in a porous layer. Acta Mechanica, 58, 125-136.
• Dey, S., Gupta, S., & Gupta, A. K. (2004). Propagation of Love waves in an elastic layer with void pores. Sādhanā, 29, 355-363.
• Biot, M. A. (1965). Mechanics of incremental deformation. John Wiley & Sons.
• Dey, S., & Chakraborty, M. (1983). Influence of gravity and initial stresses on the Love waves in a transversely isotropic medium. Geophysical Research Bulletin, 21(4), 311-323.
• Dey, S., Gupta, A. K., & Gupta, S. (2002). Effect of gravity and initial stress on torsional surface waves in dry sandy medium. Journal of Engineering Mechanics, 128, 1115-1118.
• Gupta, S., Pramanik, S., & Smita. (2021). Exemplification in exact and approximate secular equation of surface wave along distinct interfaces with sliding contact. Mechanics of Solids, 56, 819-837.
• Gupta, S., Pramanik, S., Smita, Das, S. K., & Saha, S. (2021). Dynamic analysis of wave propagation and buckling phenomena in carbon nanotubes (CNTs). Wave Motion, 104, 102730.
• Kumar, D., Kundu, S., Kumhar, R., & Gupta, S. (2020). Vibrational analysis of Love waves in a viscoelastic composite multilayered structure. Acta Mechanica, 231, 4199-4215.
• Gupta, S., Das, S., & Dutta, R. (2021). Nonlocal stress analysis of an irregular FGFPM structure imperfectly bonded to fiber-reinforced substrate subjected to moving load. Soil Dynamics and Earthquake Engineering, 147, 106744.
• Kumhar, R., Kundu, S., Pandit, D. K., & Gupta, S. (2020). Green’s function and surface waves in a viscoelastic orthotropic FGM enforced by an impulsive point source. Applied Mathematics and Computation, 382, 125325.
• Gupta, S., Das, S., Dutta, R., & Saha, S. (2021). Higher-order fractional and memory response in nonlocal double poro-magneto-thermoelastic medium with temperature-dependent properties excited by laser pulse. Journal of Ocean Engineering and Science. https://doi.org/10.1016/j.joes.2022.04.013
• Chowdhury, S., Kundu, S., Alam, P., & Gupta, S. (2021). Dispersion of Stonely waves through the irregular common interface of two hydrostatic stressed MTI media. Scientia Iranica, 28(2), 837-846.
• Maity, M., Kundu, S., Kumhar, R., & Gupta, S. (2022). An electromechanical based model for Love type waves in anisotropic-porous-piezoelectric composite structure with interfacial imperfections. Applied Mathematics and Computation, 418, 126783.
• Kumar, D., & Kundu, S. (2023). Effect of initial stresses on the surface wave propagation in highly anisotropic piezoelectric composite media. Waves in Random and Complex Media. https://doi.org/10.1080/17455030.2022.2164093
• Deringöl, A. H., & Güneyisi, E. M. (2022). Enhancing the seismic performance of high-rise buildings with lead rubber bearing isolators. Turkish Journal of Engineering, 7(2), 99-107.
• Ertuğrul, O. L., & Zahin, B. B. (2022). A parametric study on the dynamic lateral earth forces on retaining walls according to European and Turkish building earthquake codes. Turkish Journal of Engineering, 7(3), 196-207.
• Alam, P., Jena, S., Badruddin, I. A., Khan, T. M. Y., & Kamangar, S. (2021). Attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Engineering Computations. https://doi.org/10.1108/EC-07-2020-0381
• Alam, P., Singh, K. S., Ali, R., Badruddin, I. A., Khan, T. M. Y., & Kamangar, S. (2021). Dispersion and attenuation of SH-waves in a temperature-dependent Voigt-type viscoelastic strip over an inhomogeneous half-space. Journal of Applied Mathematics and Mechanics. https://doi.org/10.1002/zamm.202000223
• Alam, P., Nahid, T., Alwan, B. A., & Saha, A. (2023). Rotating radial vibrations in human bones (femoral, mandibular and tibia) and crystals (Mg, Co, Cd, Zn and beryl) made cylindrical shell under magnetic field and hydrostatic stress. Mechanics of Advanced Materials and Structures, 30(13), 2684-2700.
• Mario, J. S., & Alam, P. (2023). A multi-layered model of Newtonian viscous liquid, fiber-reinforced and poro-elastic media over a self-weighted half-space to investigate the SH-wave interactions. Mechanics of Advanced Materials and Structures. https://doi.org/10.1080/15376494.2023.2256537
• Singh, M. K., & Alam, P. (2020). Surface wave analysis in orthotropic composite structure with irregular interfaces. International Journal of Computational Mathematics. https://doi.org/10.1007/s40819-019-0745-5
• Singh, M. K., Rahul, A. K., Saha, S., Paul, S., Tiwari, R., & Nandi, S. (2024). On generalized Rayleigh waves in a pre-stressed piezoelectric medium. International Journal of Modern Physics C. https://doi.org/10.1142/S0129183124400060
• Bullen, K. E. (1940). The problem of the Earth’s density variation. Bulletin of the Seismological Society of America, 30(3), 235-250.
• Birch, F. (1952). Elasticity and constitution of the earth's interior. Journal of Geophysical Research, 57(2), 287-286.
• Cowin, S. C., & Nunziato, J. W. (1983). Linear theory of elastic materials with voids. Journal of Elasticity, 13, 125-147.
• Whittaker, E. T., & Watson, G. N. (1990). A course in modern analysis. Cambridge University Press.
• Kumar, R., & Vandana, G. (2013). Plane wave propagation in an anisotropic thermoelastic medium with fractional order derivative and void. Journal of Thermal Stresses, 1(1).
• Gubbins, D. (1990). Seismology and plate tectonics. Cambridge University Press.