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

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

Rakesh Singh Rajput (Directorate of Technical Education, India), Sunil Kumar (Rajeev Gandhi Technical University, India), Alok Chaubey (Rajeev Gandhi Technical University, India) and J. P. Dwivedi (It-Bhu, India)
Copyright: © 2011 |Pages: 17
DOI: 10.4018/jgee.2011070104
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Abstract

Non-axisymmetric dynamic response of imperfectly bonded buried orthotropic thin empty pipelines subjected to incident shear wave (SH-wave) is presented here. In the thin shell theory the effect of shear deformation and rotary inertia is not considered. The pipeline has been modeled as an infinite thin cylindrical shell imperfectly bonded to surrounding. A thin layer is assumed between the shell and the surrounding medium (soil) such that this layer possesses the properties of stiffness and damping both. The degree of imperfection of the bond is varied by changing the stiffness and the damping parameters of this layer. Although a general formulation including P-, SV-, and SH-wave excitations are presented, numerical results are given for the case of incident SH-waves only. Comparison of axisymmetric and non-axisymmetric responses are also furnished.
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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

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