Influence of Rigidity, Irregularity and Initial Stress on Shear Waves Propagation in Multilayered Media
محورهای موضوعی : Engineering
R.K Poonia
1
,
N Basatiya
2
,
V Kaliraman
3
1 - Department of Mathematics, Chandigarh University, Mohali, Punjabp-140413, India
2 - Department of Mathematics, Chandigarh University, Mohali, Punjabp-140413, India
3 - Department of Mathematics, Chaudhary Devi Lal University, Sirsa-Haryana-125055, India
کلید واژه: Rectangular irregularity, Shear waves, Anisotropic layer, Rigidity, Dispersion equation, Perturbation technique, Initial stress,
چکیده مقاله :
The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformations. The dimensionless phase velocity is plotted against dimensionless wave number for the different size of ratios of depth of rectangular irregularity with the height of the layer and anisotropy parameters with the help of MATLAB graphical routines in presence and absence of initial stress. From the graphical results, it has been seen that the phase velocity is significantly influenced by the wave number, the depth of the irregularity, rigid boundary and initial stress. The acquired outcomes can be valuable for the investigation of geophysical prospecting and understanding the cause and evaluating of damage due to earthquakes.
[1] Biot M. A., 1940, The influence of initial stress on elastic wave, Journal of Applied Physics 11(8): 522-530.
[2] Alam P., Kundu S., 2017, Influences of heterogeneities and initial stresses on the propagation of love-type waves in a transversely isotropic layer over an inhomogeneous Half-Space, Journal of Solid Mechanics 4(9): 783-793.
[3] Kundu S., Gupta S., Manna S., 2014, SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media, Meccanica 49(3): 749-758.
[4] Gupta S., Vishwakarma S.K., Majhi D.K., Kundu S., 2011, Influence of rigid boundary and initial stress on the propagation of Love wave, Applied Mathematics 2: 586-594.
[5] Kundu S., Manna S., Gupta S., 2014, Love wave dispersion in pre-stressed homogeneous medium over a porous half-space with irregular boundary surfaces, International Journal of Solids and Structures 51: 3689-3697.
[6] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2010, Effects of irregularity and anisotropy on the propagation of shear waves, International Journal of Engineering, Science and Technology 2(1): 116-126.
[7] Chattopadhyay A., Gupta S., Singh A.K., Sahu S. A., 2010, Propagation of SH Waves in an Irregular Non Homogeneous Monoclinic Crustal Layer over a Semi-Infinite Monoclinic Medium, Applied Mathematical Sciences 4(44): 2157-2170.
[8] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2010, Effects of irregularity and anisotropy on the propagation of shear waves, International Journal of Engineering Science and Technology 2(1): 116-126.
[9] Rouze N. C., Wang M. H., Palmeri M. L., Nightingale K. R., 2013, Finite element modeling of impulsive excitation and shear wave propagation in an Incompressible, transversely isotropic medium, Journal of Biomechanics 46(16): 2761-2768.
[10] Vaishnav P.K., Kundu S., Abo-Dahab S.M., Saha A., 2017, Torsional surface wave propagation in anisotropic layer sandwiched between heterogeneous half-space, Journal of Solid Mechanics 9(1): 213-224.
[11] Biot M.A., 1956, Theory of propagation of elastic waves in a fluid saturated porous solid, The Journal of the Acoustical Society of America 28: 335-354.
[12] Biot M.A., Willis D.G., 1957, Elastic coefficients of the theory of consolidation, The Journal of the Acoustical society of America 24: 594-601.
[13] Konczak Z., 1988, On propagation of shear waves in a multilayered medium including a fluid saturated porous stratum, Acta Mechnica 79: 169-181.
[14] Kumar R., Madan D. K., Sikka J.S., 2014, Love wave propagation in an irregular fluid saturated porous anisotropic layer with rigid boundary, Journal of Applied Sciences Research 10(4): 281-287.
[15] Kumar R., Madan D.K., Sikka J. S., 2015, Effect of irregularity and inhomogeneity on the propagation of love waves in fluid saturated porous isotropic layer, Journal of Applied Science and Technology (JAST) 20(1-2): 16-21.
[16] Kaliraman V., Poonia R.K., 2018, Elastic wave propagation at imperfect boundary of micropolar elastic solid and fluid saturated porous solid half-space, Journal of Solid Mechanics 10(3): 655-671.
[17] Poonia R.K., Madan D.K., Kaliraman V., 2019, Rigidity and irregularity effect on surface wave propagation in a fluid saturated porous layer, Journal of Solid Mechanics 11(4): 886-901.
[18] Gupta S., Chattopadhyay A., Majhi D.K., 2010, Effect of initial stress on propagation of love wave in an anisotropic porous layer, Journal of Solid Mechanics 2(1): 50-62.
[19] Kumar R., Madan D.K., Sikka J.S., 2014, Shear wave propagation in multilayered medium including an irregular fluid saturated porous stratum with rigid boundary, Advances in Mathematical Physics 2014: 163505.
[20] Kumar R., Madan D.K., Sikka J.S., 2016, Effect of rigidity and inhomogeneity on the propagation of Love waves in an irregular fluid saturated porous isotropic layer, International Journal of Mathematics and Computation 27(2): 55-70.
[21] Prasad R.M., Kundu S., 2019, Dispersion of torsional surface wave in a pre-stressed heterogeneous layer sandwiched between anisotropic porous half-spaces under gravity, Journal of Solid Mechanics 11(4): 707-723.
[22] Poonia R.K., Sonu Kaliraman V., Kumar P., 2019, Surface wave propagation under initially stressed porous medium, International Journal on Emerging Technologies 10(2): 48-53.
[23] Poonia R. K., Kharb K., Madan D. K., 2019, Rigidity effects on surface waves in multilayered media, International Journal on Emerging Technologies 10(2): 69-72.
[24] Ewing W.M., Jardetzky W.S., Press F., 1957, Elastic Waves in Layered Media, McGraw-Hill, New York.
[25] Biot M.A., 1955, Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics 26(2): 182-185.
[26] Willis H.F., 1948, A formula for expanding an integral as a series, Philosophical Magazine 39: 455-459.
[27] Tranter C.J., 1966, Integral Transform in Mathematical Physics, Methuen.
[28] Ding H., Chen W., Zhang L., 2006, Elasticity of Transversely Isotropic Materials, Springer.
