Non-Axisymmetric Dynamic Response of Imperfectly Bonded Buried Orthotropic Thin Empty Cylindrical Shell Due to Incident Shear Wave (SH Wave)

2. Basic Equations And Formation

The cylindrical pipeline has been modeled as an infinitely long cylindrical shell of mean radius R and thickness h. It is considered to be buried in a linearly elastic, homogeneous and isotropic medium of infinite extent. Basic approach of the formulation is to obtain the mid plane displacements of the shell by solving the equations of motion of the orthotropic shell. Traction terms in the equations of motion are obtained by solving the three-dimensional wave equation in the surrounding medium. Appropriate boundary conditions are applied at the shell surfaces. Equations arising out of boundary conditions along with the equations of motion of the shell are simplified to yield a response equation in matrix form. Equation governing the non axis-symmetric motion of an infinitely long orthotropic cylinder has been derived (Figure 1) following the approach of Herrmann and Mirsky (1957).

Figure 1.

Geometry of problem