Control of a flexibly supported continuous pipeline excited by a spatially distributed earthquake input

Pipelines represent a critical component within civil engineering infrastructure systems. The importance of maintaining the integrity of water, natural gas, and petroleum pipelines during and immediately following a seismic event has been well documented. Such above-ground sections may be supported by semi-rigid as well as relatively flexible supports over large distances. Previous research in this area has assumed that the support structures are rigid, allowing very simple approximations to be made.; The current research first obtains the equations of motion for a long pipeline with supports modeled as spring-dampers in the transverse horizontal and vertical directions. The eigenvalues and eigenfunctions of the support-pipeline system for the no-flow condition are determined, and the effect of varying the ratio of the stiffness of the supports to the rigidity of the pipe over a wide range representing very flexible to very stiff supports is investigated. Stiffness ratios representing actual pipeline systems indicate that previous assumptions leading to simple mode shapes are not supported. The linear equations of motion are solved using an approximate approach in which the no-flow eigenfunctions are used as modal expansion functions. The optimal passive support damping values as a function of the various system parameters and frequency content of the input excitation are determined. Pipelines with representative numbers of supports are simulated over a wide range of stiffness ratios, fluid flow velocities, and support damping values to determine maximum dynamic response. To investigate longer pipelines, the maximum extent along the pipeline that a support excitation may cause appreciable response is examined as a function of pipeline/support stiffness and number of supports. The spatially distributed earthquake input is then incorporated into the model, determining the response as a function of seismic excitation propagation time between supports.; A two support flexible pipeline is tested on the shaking table to verify a specific application of the system model as well as the response of the system to specific combinations of support stiffness and damping parameters. An active control strategy which incorporates shape control and direct output feedback control, acting in parallel, is developed and simulation results are obtained. The control is applied to a candidate pipeline, and the maximum required control forces are determined as a function of the input excitation, and as a function of the number of supports in the pipeline.