Vibrational analysis of Love waves in a viscoelastic composite multilayered structure
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O R I G I NA L PA P E R
Dharmendra Kumar Shishir Gupta
· Santimoy Kundu · Raju Kumhar ·
Vibrational analysis of Love waves in a viscoelastic composite multilayered structure
Received: 18 December 2019 / Revised: 29 March 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract A unified procedure is presented to investigate the dispersion and damping behavior of Love waves in a double-layered structure. The double-layered structure is comprised of a viscoelastic fiber-reinforced medium (Medium I) embedded between a viscoelastic sandy layer (Medium II) and a viscoelastic porous semi-infinite medium (Medium III). The displacement vectors for the respective medium have been obtained using analytical techniques. Using the separation of variables method and admissible boundary conditions at the free surface and the interfaces, the complex frequency equation is obtained in closed form. The substantial impact of all material parameters involved in the considered model on the phase velocity as well as damped velocity has been observed numerically and shown by graphical illustrations. The outcomes from this analysis may serve as a dynamic tool in various fields including geophysics, geotechnical, and earthquake engineering.
1 Introduction The study of seismic waves is very much important for the researchers and seismologists, due to the enormous applications in the field of seismology, geophysics, and earthquake engineering. To analyze the dynamic construction of the Earth, seismic actions are applied. The complex structure of the Earth contains various materials like rocks, soil, grains or platelets, etc., with different material properties like sandiness, fiberreinforcement, porosity, etc. Some well- known authors investigated the propagation of seismic waves inside and on the surface of the Earth to obtain the basic idea of elastic waves, in their treatises like Love [27], Biot [12], and Gubbins [19], and many more. Seismic waves in the layered structure of the Earth were examined by Ewing et al. [18]. It is well-known for the researchers and geologists that the physical properties of the material inside the Earth are not the same everywhere. Some elastic materials are buried inside the layer of the Earth e.g., bitumen, coal tar, amorphous polymers, salt, sediments, etc., exhibiting both viscous as well as elastic properties and hence, these are termed as viscoelastic materials. Viscoelastic materials are time-dependent. When transient loads are applied on the viscoelastic materials, they have a unique equilibrium configuration, and after the removal of transient load, it recovers automatically. The study of physical properties and the viscoelastic behavior of these materials has been of practical and perpetual interest in various contexts. These materials have a wide range of applications in structural and engineering sciences and in various design processes to achieve particular goals. Viscoelasticity is one of the interesting phenomena in some branches like material science, metallurgy, and sol
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