Authors:
Suparna Roychowdhury,AbhijitPramanik,Mostaid Ahmed,DOI NO:
https://doi.org/10.26782/jmcms.2024.10.00006Keywords:
Fiber-reinforced,Inhomogeneous,Love wave,Non-local elasticity,Abstract
An analytical technique employing the variable separable method has been used in an attempt to precisely grasp and assess the impact of the property non-local elasticity upon the wave transmission response of an anisotropic fiber-reinforced material embedded over a semi-infinite, inhomogeneous medium that changes linearly. As depth increases, the stiffness and density of a semi-infinite substrate are believed to alter linearly. Availing the Whittaker function, a relation about dispersion has been acquired to analyze the response of SH waves. The visual representation depicts a significant influence of non-local elasticity on the propagation of SH-wave modes. Special cases have been found assessing the concurrency of the model with the original form equation of Love wave. The effects of non-locality, fiber-reinforcement parameters, and inhomogeneity parameters carry implications in designing and gradation of material characteristics some important parameters on the wave characteristics of the studied model.Refference:
I. Abd-Alla AM. and Ahmed SM. : ‘Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium.’ Applied Mathematics and Computation. Vol. 106(2), pp. 265–275, 1999. 10.1016/S0096-3003(98)10128-5
II. Abd-Alla AM., Hammad HAH. and Abo-Dahab SM. : ‘Rayleigh waves in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field.’ Applied Mathematics and Computation. Vol. 154, pp. 583–597, 2004. 10.1016/S0096-3003(03)00767-7
III. Abd-Alla AM., Nofal TA., Abo-Dahab SM., Al-Mullise A. : ‘Surface waves propagation in fiber-reinforced anisotropic elastic media subjected to gravity field.’ Int J Phys Sci. Vol. 2013;8(14), pp. 574–84. 2004. 10.5897/IJPS2013.3812
IV. A. C. Eringen and D. Edelen. : ‘On nonlocal elasticity.’ Int. J. Eng. Sci. Vol. 10(3), pp. 233–248, 1972.
V. A. C. Eringen. : ‘Screw dislocation in non-local elasticity.’ J. Phys. D Appl. Phys. 10(5), pp. 671, 1977.
VI. A. C. Eringen : ‘Theory of nonlocal elasticity and some applications.’ Princeton University, Department of Civil Engineering, Princeton, NJ. 1984.
VII. A. C. Eringen and J. L. Wegner. : ‘Nonlocal continuum field theories’ Appl. Mech. Rev. 56(2), pp. B20–B22, 2003.
VIII. Ahmed SM. and Abo-Dahab SM. : ‘Propagation of Love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium.’ Journal of Vibration and Control. 16(12): pp. 1845–1858, 2010. 10.1177/1077546309341154
IX. Andrianova ZS. : ‘Seismic love waves.’ Springer Science & Business Media. 2012.
X. Biot M. A. : ‘Mechanics of Incremental Deformations.’ Wiley, New York. 1965.
XI. Chattopadhyay A (1975) On the dispersion equation for Love wave due to irregularity in the thickness of non-homogeneous crustal layer. Acta Geophysica Polonica 23: 307–317.
XII. Chakraborty SK and Dey S (1982) The propagation of Love waves in water saturated soil underlain by heterogeneous elastic medium. Acta Mechanica 44: 169–176. 10.1007/BF01303335
XIII. Chattaraj R, Samal SK. Love waves in the fiber-reinforced layer over a gravitating porous half-space. Acta Geophys 2013;61(5):1170–83. 10.2478/s11600-012-0100-2
XIV. D. G. B. Edelen, A. E. Green, and N. Laws, Nonlocal continuum mechanics, Arch. Ration. Mech. Anal. 43 (1971), no. 1, 36–44.
XV. Dey S, Gupta S and Gupta AK (1996) Propagation of Love waves in heterogeneous crust over a heterogeneous mantle. Journal of Acta Geophysica Polonica XLIX (2): 125–137.
XVI. Dey S, Gupta S and Gupta AK (2004) Propagation of Love waves in an elastic layer with void pores. Sadhana 29: 355–363. 10.1007/BF02703687
XVII. D. Karlicic, T. Murmu, S. Adhikari, and M McCarthy, Non-local structural mechanics, John Wiley & Sons, New York, USA, 2015.
XVIII. Eskandari M, Shodja HM. Love waves propagation in functionally graded piezoelectric materials with quadratic variation. J Sound Vib 2008;313(1-2): 195–204. 10.1016/j.jsv.2007.11.037
XIX. Gubbins D. Seismology and plate tectonics. Cambridge University Press; 1990.
XX. Gupta S, Ahmed M. On propagation of Love waves in dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space. Earthq Struct 2017;12(6):619–28. 10.12989/eas.2017.12.6.619
XXI. Gupta S, Vishwakarma SK, Majhi DK, Kundu S. Possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities. Appl Math Model 2013; 37(10-11) : 6652–60. 10.1016/j.apm.2013.01.008
XXII. Kalyani VK, Sinha A, Pallavika, et al. (2008) Finite difference modeling of seismic wave propagation in monoclinic media. Acta Geophysica 56(4): 1074–1089. 10.2478/s11600-008-0049-3
XIII. Kundu S, Kumari A, Gupta S, Pandit DK. Effect of periodic corrugation, reinforcement, heterogeneity and initial stress on Love wave propagation. Waves Random Complex Media 2016;26(4):485–515. 10.1080/17455030.2016.1168951
XIV. Kundu S, Gupta S, Manna S, Dolai P. Propagation of Love wave in fiber-reinforced medium over a nonhomogeneous half-space. Int J Appl Mech 2014;6(5):1450050. 10.1142/S1758825114500501
XV. Kuznetsov SV. Love waves in layered anisotropic media. J Appl Math Mech 2006; 70(1):116–27. 10.1016/j.jappmathmech.2006.03.004
XVI. Love AEH. Some problems of geodynamics. London: Cambridge University Press; 1911.
XVII. Liu JX, Fang DN, Wei WY, Zhao XF. Love waves in layered piezoelectric/ piezomagnetic structures. J Sound Vib 2008;315(1-2):146–56. 10.1016/j.jsv.2008.01.055
XVIII. Markham MF. Measurement of the elastic constants of fiber composites by ultrasonics. Composites 1970;1(3):145–9.
XIX. M. N. L. Narasimhan and B. M. McCay, Dispersion of surface waves in nonlocal dielectric fluids, Arch. Mech. 33 (1981), no. 3, 385–400.
XXX. Manna S, Kundu S, Gupta S. Effect of reinforcement and inhomogeneity on the propagation of Love waves. Int J GeoMech 2016;16(2):04015045. 10.1061/(ASCE)GM.1943-5622.0000517
XXXI. Manna S, Kundu S, Gupta S. Propagation of love waves in piezoelectric layered system over an isotropic half-space under initial stress. In: Conference GSI; 2016. p. 74–9. 10.17491/cgsi/2016/95898
XXXII. Manna, S. and Bhat, M., 2022. Love wave fields in a non-local elastic model with reinforced and inhomogeneous media. Soil Dynamics and Earthquake Engineering, 161, p.107388. 10.1016/j.soildyn.2022.107388
XXXIII. Manna, S., Kundu, S. and Gupta, S., 2015. Love wave propagation in a piezoelectric layer overlying in an inhomogeneous elastic half-space. Journal of Vibration and Control, 21(13), pp.2553-2568. 10.1177/1077546313513626
XXXIV. Pradhan A, Samal SK, Mahanti NC. Influence of anisotropy on the love waves in a self-reinforced medium. J Appl Sci Eng 2003;6(3):173–8. 10.6180/jase.2003.6.3.06
XXXV. Son MS, Kang YJ. Propagation of shear waves in a poroelastic layer constrained between two elastic layers. Appl Math Model 2012;36(8):3685–95. 10.1016/j.apm.2011.11.008
XXXVI. S.B. Altan, Uniqueness in the linear theory of nonlocal elasticity, Bull. Tech. Univ. Istanb 37 (1984), 373–385.
XXXVII. S. B. Altan, Existence in nonlocal elasticity, Archiwum Mechaniki Stosowanej 41 (1989), no. 1, 25–36.
XXXVIII. Wang Q, Quek ST, Varadan VK. Love waves in piezoelectric coupled solid media. Smart Mater Struct 2001;10(2):380. 10.1088/0964-1726/10/2/325