Abstract
Engineering methods for finding the average (averaged) velocity of propagation of longitudinal waves in pipelines with flexible joints are presented. By accurate analysis of the problem of oscillations of a one dimensional periodically inhomogeneous structure it is shown that the results of engineering approaches for rod velocity are the first or long-wave asymptotic approximation which valid when the period of external influence (the length of the seismic wave) significantly exceeds the size of the periodicity cell of the pipeline (the length of the pipe with a joint). Thus, it is established that when this condition is met, the problem of pipeline dynamics with joints is reduced to a much simpler problem of vibrations of a homogeneous pipeline, the velocity of wave propagation in which is equal to the found average value. Numerical examples are given that demonstrate a significant (sometimes by an order of magnitude) decreasing of the rod velocity in the presence of flexible joints.
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