The effect of viscosity and heterogeneity on propagation of G-type waves

• Autorzy: Gupta S. , Smita

Identyfikatory

DOI

10.1515/amcs-2017-0018

• Języki publikacji: EN

Abstrakty

EN

Earthquakes yield motions of massive rock layers accompanied by vibrations which travel in waves. This paper analyses the possibility of G-type wave propagation along the plane surface at the interface of two different media which is assumed to be heterogeneous and viscoelastic. The upper layer is considered to be viscoelastic and the lower half space is considered to be an initially stressed heterogeneous half space. The dispersion equation, as well as the phase and group velocities, is obtained in closed form. The dispersion equation agrees with the classical Love type wave. The effects of the nonhomogeneity of the parameters and the initial stress on the phase and group velocities are expressed by means of a graph.

Słowa kluczowe

EN

G-type wave; dispersion equation; heterogeneity

PL

fala typu G; równanie dyspersji; niejednorodność

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 2
• Strony: 253--260
• Opis fizyczny: Bibliogr. 16 poz., rys., wykr.

Twórcy

autor

Gupta S.

• Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India

autor

Smita

• Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India

Bibliografia

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• [2] Belfield, A.J., Roger, T.G. and Spencer, A.J.M. (1983). Stress in elastic plates reinforced by fibres lying in concentric circles, Journal of the Mechanics and Physics of Solids 31(1): 25–54.
• [3] Chattopadhyay, A. and Keshri, A. (1986). Generation of G-type seismic wave under initial stress, Indian Journal of Pure and Applied Mathematics 17(8): 1042–1055.
• [4] Chattopadhyay, A., Choudhary, S. (1990). Propagation, reflection and transmission of magnetoelastic shear waves in a self reinforced medium, International Journal of Engineering Science 28(6): 485–495.
• [5] Chattopadhyay, A., Gupta, S., Sharma, V.K. and Kumari, P. (2010). Propagation of G-type seismic waves in viscoelastic medium, International Journal of Applied Mathematics and Mechanics 6(9): 63–75.
• [6] Chattopadhyay, A. and Singh, A.K. (2012). G type seismic waves in fibre reinforced media, Meccanica 47(7): 1775–1785.
• [7] Gutenberg, B. (1953). Wave velocities at depths between 50 and 600 kilometers, Bulletin of the Seismological Society of America 43(3): 223–232.
• [8] Gutenberg, B. (1954). Effects of low velocity layers, Geofisica Pura E Applicata 29(1): 1–10.
• [9] Hool, G.A. and Kinne, W.S. (1924). Reinforced Concrete and Masonry Structure, Mc Graw Hill, New York, NY.
• [10] Kundu, S., Gupta, S. and Manna, S. (2014). Propagation of G-type seismic waves in heterogeneous layer lying over an initially stressed heterogeneous half space, Applied Mathematics and Computation 234: 1–12.
• [11] Kaur, T., Sharma, S.K. and Singh, A.K. (2016). Shear wave propagation in vertically heterogeneous layer over a micropolar elastic half space, Mechanics of Advanced Materials and Structures 24(2): 1–27.
• [12] Lehman, L. (1961). S waves and the structure of the upper mantle, Geophysical Journal of the Royal Astronomical Society 3: 529–538.
• [13] Mal, A. K. (1962). On the generation of G-waves, Journal of Geophysical Research 72(2): 82–88.
• [14] Sato, Y. (1952). Study on surface waves, VI generation of Love and other type of SH waves, Bulletin of the Earthquake Research Institute, University of Tokyo 30: 101–120.
• [15] Valeev, K.G. (1961). On Hill’s method in the theory of linear differential equations with periodic coefficients, Journal of Applied Mathematics and Mechanics 24(6): 1493–1505.
• [16] Vishwakarma, S.K., Xu, R. (2016). G-type dispersion equation under suppressed rigid boundary: Analytic approach, Applied Mathematics and Mechanics 37(4): 501–512.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).