Spatial vibrations of eflical heal-exchange pipes excited by internal flow of a heat carrier

Abstract

The principal result of the present work is that on the basis of the variational principle of Hamilton-Ostrogradskii we obtained a complete system of differential equations of the vibrations of helical heat exchange pipes excited by internal flow of the heat carrier, and the analytical formulation of the set of all permissible boundary conditions is provided. It was shown that from the presented system there follow as special cases many results obtained earlier in connection with curved and straight pipes and spatial rods. It was established that depending on the conditions of constraint of the ends of a heat exchange pipe, the system may be conservative or nonconservative. In the former case, loss of stability may be in flexural form when the critical flow rate is exceeded, in the latter case it is the flutter form. We examined actual examples of conservative and nonconservative systems, and we formulated boundary-value problems for them. The suggested equations and dependences may be the basis for further improvement of the theory of vibrations of spatial heat exchange pipes excited by a flow of heat carrier, by taking additionally into account the viscosity of the liquid, the nonsteady state of the flow, the initial stresses in the pipe, the rotary inertia of its sections, damping, and other factors in dependence on the problem under examination and the accuracy required for the actual applications. On the other hand, being very general, the equations and dependences may find applications of their own in practical engineering calculations.