Non-linear dynamic analysis of piping system using the pseudo force method

Simple piping systems are composed of linear elastic elements and can be analysed using conventional linear methods. The introduction of constraint springs, separated from the pipe with clearance gaps, to such systems to cope with the pipe whip or other extreme excitation conditions introduces non-linearities to the system, such non-linearities being associated with the gaps. Since these spring-damper constraints are usually limited in number, discretely located and produce only weak non-linearities, the analysis of linear systems including these non-linearities can be carried out by using modified linear methods. In particular, the application of pseudo force methods, wherein the non-linearities are treated as displacement-dependent forcing functions acting on the linear system, was investigated.The non-linearities induced by the constraints are taken into account as generalised pseudo forces on the right-hand side of the governing dynamic equilibrium equations. Then an existing linear elastic finite element piping code, EPIPE, was modified to permit application of the procedure. This option was inserted such that the analysis could be performed using either the direct integration method or via a modal superposition method, the Newmark-Beta integration procedure being employed in both methods. The modified code was proof tested against several problems taken from the literature or developed with the non-linear dynamics code, OSCIL. The problems included a simple pipe loop, a cantilever beam and a lumped mass system subjected to pulsed and periodic forcing functions. The problems were selected to gauge the overall accuracy of the method and to ensure that it properly predicted the jump phenomena associated with non-linear systems.Implementation of the method was found to be straightforward with the simplest iteration procedure for the pseudo force vector sufficing. The results predicted with the method agreed in all important aspects with existing solutions as well as those generated with other methods. As with linear analyses, the modal superposition solution mode was found to be the most efficient; however, exhibiting slightly greater inaccuracies.