Research Projects

This project aims to explore the mathematical aspects of wave propagation in isotropic or anisotropic media using the combined theory of nonlocal thermoelasticity. The study focuses on different types of interfaces and the phenomenon of wave scattering in composite layered structures. The primary objective is to develop more realistic mathematical models to understand the behavior of seismic waves in complex layered structures of the Earth. The study of distinct phenomena of seismic waves in composite layered structures has been an area of perpetual interest in the dynamic era to bring out the latent characteristics of waves propagating through such structures. The study of seismic waves through the Earth medium is a core aspect of seismology where we investigate seismic (elastic) wave propagation in different layered structures of the Earth. By employing theoretical assumptions for the dynamics of continuum bodies, solid mechanics and applied mathematical methods, new mathematical models based on different theories are developed and applied to problems. The main thrust of theoretical seismology is to develop and improve various techniques for modeling regional and global geophysical processes and determining the three-dimensional structure of the Earth. Seismology has produced a remarkably sharp picture of the Earth's interior by analyzing seismic wave propagation through different layers of the Earth combining techniques and data from multiple disciplines such as Physics, Mathematics, Geophysics, and Geology. Geophysical studies have established that the Earth is an initially stressed medium with a considerably anisotropic and heterogeneous interior, where elastic properties like stiffness and density vary with depth. The Earth comprises different types of materials which may be isotropic or anisotropic, homogeneous or heterogeneous, and elastic or viscoelastic. The interfaces (boundaries) between these layers may be perfect or imperfect, bonded or unbonded, compressible or incompressible, as indicated by parameter differences between two interface layers. In this context, our work focuses on the elastic wave responses in anisotropic media (e.g., triclinic, monoclinic, orthotropic, transversely isotropic, magnetoelastic, viscoelastic, fiber-reinforced, poro-elastic, piezoelectric, double poro-elastic, slightly compressible, incompressible, micropolar, etc.), which differ significantly from those in isotropic media. This project aims to address gaps in the existing literature by developing more realistic mathematical models to study the response of moving loads, inclined loads, surface wave propagation and the reflection and transmission of seismic waves in composite nonlocal thermoelastic layered structures.