Abstract
A one-dimensional statement of unsteady wave problem of a longitudinal monochromatic wave propagation and reflection from a rigid stationary barrier to which an underground pipeline abuts is given. The linear viscoelastic Eyring model, which describes limited creep and limited relaxation, is taken as the pipeline strain law. Eyring model allows us to describe the behavior of underground steel and polymer pipelines under dynamic loading. The problem is solved numerically using the theory of characteristics, followed by the finite difference method in an implicit scheme. Numerical solutions obtained in the form of dependences of plane wave parameters: longitudinal stress, velocity and strain for fixed sections of the pipeline are analyzed in the paper. An analysis of changes in these wave parameters shows that at high frequencies of dynamic load generating the wave, the stress amplitude in the pipeline increases by two or more times compared to the load amplitude. This is due to the superposition of incident and reflected waves in the pipeline and to a high loading rate of the pipeline. At low frequencies of dynamic loading, such an increase is not observed due to the low loading rate. The obtained numerical solutions allow choosing the statement of problems on dynamic stress state of an underground pipeline depending on the frequency of incident wave. It is shown that the greatest longitudinal stress in an underground pipeline arises in points (sections) close to its connection with a rigid stationary solid body.
Published Version
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