CRITICAL VELOCITIES OF ELASTICALLY RESTRAINED MULTI-SPAN FLUID CONVEYING PIPES RESTING ON CONTINUOUS ELASTIC FOUNDATION

摘要

The effect of flow velocity on the natural frequencies of straight pipe conveying fluid are of considerable practical importance. In general, it is found that the natural frequency of vibration decreases with increasing values of flow velocity and this effect may be very important in industrial systems involving high fluid velocities through flexible thin-walled pipes. If the flow velocity reaches a critical value, the effective natural frequency becomes zero, which leads to pipe buckling. From a detailed literature search carried out, it is observed that most of the investigators have considered the dynamic behaviour of single-span pipes conveying fluid only and very few studies are made on multi-span pipes. The present paper deals with multi-span Bernoulli-Euler pipes conveying fluid with elastic restraints against rotation at either ends and resting on an elastic foundation. As an example, a two-span pipe conveying fluid with hinge-type boundary conditions at the intermediate support is dealt with in detail. Finite element equations have been formulated and a computer program has been developed to calculate the non-dimensional critical flow velocity parameter. Numerical results are presented for varying values of non-dimensional pipe and restraint stiffness parameters. Interesting conclusions are drawn based on the results obtained.