The Investigation of Torsional Waves Propagation in a Sandwiched and Initially Stressed Dry Sandy Gibson Poroelastic Dissipative Isotropic Solid

Résumé

In this paper, torsional waves in sandwiched solids are investigated in the framework of Biot’s incremental theory. The solid consists of dry sandy Gibson poroelastic dissipative isotropic cylindrical solid sandwiched between two heterogeneous isotropic poroelastic cylindrical solids, all are initially stressed. The solutions for the problems of torsional waves in upper heterogeneous poroelastic cylindrical solid, dry sandy Gibson poroelastic cylindrical middle solid, and lower heterogeneous poroelastic cylindrical solids are presented. The solution of the problem reduced to that of Whittaker’s differential equation. Frequency equation is obtained from the boundary conditions of displacement components and stresses which are assumed to be continuous at the interfaces between upper solid and middle, and middle solid and lower solid. The solid under consideration is dissipative, the frequency equation is implicit and complex valued. Employing the values in the frequency equation, the frequency and attenuation coefficient against heterogeneous parameter at fixed sandy parameter, gravity parameter and initial stress are computed. The values are computed using the bisection method implemented in MATLAB. Wave characteristics namely, frequency and attenuation coefficient are computed against heterogeneity at fixed initial stresses, Sandy parameter, gravity parameter, and numerical results are presented in graphs.