Three-dimensional Green’s function approach for analysis of dispersion and attenuation curve in fibre-reinforced heterogeneous viscoelastic layer due to a point source

Santimoy Kundu, Alka Kumari and Shishir Gupta

Applied Mathematics and Computation, 2018, vol. 338, issue C, 387-399

Abstract: The present paper deals with the propagation of Love waves due to the presence of a point source in the fibre-reinforced heterogeneous viscoelastic medium with the aid of Green’s function technique. The physical parameters, i.e. rigidity and density are assumed to be exponentially and linearly varying function of depth for medium and half-space, respectively. Three-dimensional Green’s function representation for stresses and displacements are derived in complex-plane line-integral. The frequency equations of Love-type waves are derived relating the dependence complex wave numbers after developing the mathematical model with the help of Green’s function and Fourier transformation. This representation is useful in various elastodynamic as well as elastostatic problems. The complex expansion of frequency equation is derived to define the phase velocity and attenuation coefficient of Love waves in the proposed model. Dispersion and attenuation curves are plotted by taking different variations in the reinforcement, inhomogeneity and viscoelastic parameters. The results indicate that the effect of these parameters are very pronounced. The final conclusion can be used to understand the nature of propagation of Love waves in the introduced model.

Keywords: Green’s function; Heterogeneity; Fibre-reinforcement; Viscoelasticity; Attenuation coefficient; Dispersion relation (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318303230
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:338:y:2018:i:c:p:387-399

DOI: 10.1016/j.amc.2018.04.011

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().