ANALYTICAL SOLUTIONS OF WAVES IN AN INITIALLY STRESSED CORRUGATED 2-D HOMOGENEOUS TRANSVERSELY ISOTROPIC HALF-SPACE WITH THERMAL AND INCLINED MECHANIZATIONS
Keywords:
Mechanical inclination, transversely isotropic, symmetric matrix material, initial Stress, Corrugation, thermal fieldAbstract
Oftentimes, we witness modulations of waves on pre-stressed materials due to internal or environmental factors like the thermal energy, and of which these require interpretations. These interpretations are hinged on models that would evidently give analytical or numerical solutions which in turn could result to experimental studies and validations. Consequently, this current study presents a closed-form mathematical solution for plane surface wave propagation in a transversely isotropic material with a corrugated boundary, initial stress, and thermal flux under inclined mechanical loading. The Green-Lindsay theory of thermo-elasticity consisting of two relaxation times thermal parameters is taken into account. The normal mode approach of wave analysis for the analytical solution of the modeled problem is conceptualized and employed in a 2-D component dynamics and analysis. This stems from the fact that the model hyperbolic equation is satisfied and it is the wave equation. And by utilizing appropriate grooved boundary conditions in the form of Fourier trigonometric series which infuses elements of initial stress parameters via the normal stress components, we derived closed-form analytical solutions of the dynamic fields of; stress profiles, thermal field distribution and the displacement relations. We deduce the dependency of the interacting physical parameters of initial stress, angle of inclination, and corrugated parameters on the dynamics of the model field distributions. This research work would play a host to information regarding the Mathematical formulations and analytical results associated with geophysical, seismological examinations and mechatronics wave solutions on materials. Also, due to evolving technology, variable modulation of the grooved parameters for a stressed transversely isotropic material would be paramount for both analytical and experiment-based studies.
