Analogy of a Linear Chain and Seismic Vibrations of Segmental and Viscoelastic Pipelines

In the problem of seismic vibrations of a segmental pipeline with damping joints, deformed by the law of linear viscoelasticity, an original analogy with a linear chain of concentrated masses was put forward. The constructed discrete system generalizes the monatomic lattice model in the sense that the viscoelastic interaction between the masses of the chain is considered and, moreover, the forced (and not own) oscillations of such a system are investigated. By the transition from a discrete system to a continuous one, the integro-differential oscillation equation of a segmented pipeline with viscoelastic joints in an elastically resisting medium is obtained. This equation is a generalization of the well-known Klein–Gordon differential equation describing the “constrained” vibrations of an elastic rod or string in a medium with elastic resistance. In addition, the equation gives the problem of seismic vibrations of a continuous pipeline from a polymer (viscoelastic) material.