Attenuation and dispersion characteristic of Rayleigh waves in a compressed viscoelastic strip: a comparative study
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ORIGINAL ARTICLE
Attenuation and dispersion characteristic of Rayleigh waves in a compressed viscoelastic strip: a comparative study Manoj Kumar Singh1 • Parvez Alam2 Received: 11 September 2019 / Accepted: 5 February 2020 Sociedad Matemática Mexicana 2020
Abstract The present study develops the dispersion and attenuation characteristics of Rayleigh wave regulations through a pre-stressed Voigt type viscoelastic strip of finite thickness. The displacement expressions of Rayleigh wave in the strip are introduced. The complex frequency equation of the wave motion is thus obtained. We have studied the effects of initial stress, attenuation coefficients and dissipation factor on the phase and damped velocities simultaneously. Keywords Attenuation coefficient Dissipation factor Phase velocity Damping velocity
Mathematics Subject Classification 74J15 74L10 74Dxx 74E05
1 Introduction Viscoelasticity means the combination of viscosity and elasticity; it is a special characteristic of materials that display both viscous and elastic behaviour when subjected to distortion. The most determining attribute of the viscoelastic materials is their ability to absorb the high amount of energy produced during volcanic eruptions and earthquakes. Hence, to withstand the tremors during an earthquake, some of the metal alloys possessing viscoelastic property are utilized as dampers in the construction of multi-storey buildings. Therefore, the study of seismic waves through viscoelastic structures has become a matter of interest among several & Parvez Alam [email protected] 1
Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, AP 517325, India
2
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
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M. K. Singh, P. Alam
geophysicists and seismologists worldwide [1–3]. Recently, Saha et al. [4] investigated the phase velocity variation on the Raylegh wave propagation in a pre-stressed medium. It is well known that the Earth is a pre-stressed medium. A large quantity of initial stress may generate in the Earth because of several natural and artificial phenomena such as difference in gravity, temperature, weight, manufacturing activities, differential external forces, slow process of creep, hydrostatic tension or compression, presence of overburdened layer, external loading etc. Researchers and seismologists mostly favour the pre-stressed structure to analyse the underground response of seismic surface waves. Some exemplary works on initially stressed media were acknowledged by several authors including [5–8]. The assumption of Voigt-type viscoelastic surface stratum of the earth resting on an extremely rigid foundation creates a strong basis for the consideration in the study of geomechanical problems. The main aim of this paper is to study the Rayleigh wave propagation through a Voigt-type viscoelastic layer of finite thickness resting over a rigid foundation. A complex frequency equation for the wave pro
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