Mathematical Simulation and Solution of the Problem of Seismo–Dynamics of Underground Pipelines

Mathematical modeling and numerical solution of problems of underground pipelines under spatial seismic effects are discussed in the paper. The systems of differential equations of motion are obtained for the problems of seismodynamics of underground pipelines with complex conditions of interacting with soil, at arbitrary direction of seismic load, based on Hamilton-Ostrogradsky variation principle, this allows in general form to consider a number of classes of problems. An analysis of results was made for an extended pipeline with joints located on the Oxy plane and interacting with surrounding soil. Applied software was created for calculation and visual representation of the results of solving problems in the form of graphs of changes in displacements, forces and moments over time at selected nodal points of the structure and in the form of animation. Results obtained present a new contribution into seismodynamic theory; they open wide possibilities for their use in optimal design of the complex of life support in seismic zones.

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