Vibrations of the underground pipeline in the vertical plane considering the rotational inertia and transversal shear

Abstract

The subject of the study is the underground pipeline vibration in a vertical plane, considering the inertia of rotation and transverse shear. A system of differential equations of motion of an underground pipeline with natural boundary and initial conditions under spatial seismic loading is derived in the article. From the formulas obtained, it is necessary to determine the internal forces in the sections of the underground structure. Research methods are based on the variational equation of seismic loading of underground structures in a matrix form; methods of mathematical modeling and numerical methods for their solutions An algorithm and a program for the numerical solution of the resulting system of equations are compiled. Having determined the displacements, the internal forces in the sections of the underground pipeline are defined. The influence of the inertia of rotation of the section and the transverse shear on the values of displacements and force factors of the pipe is studied. Calculation results are given.