An iterative approach for the dynamic analysis of piping systems with nonlinearities in the support system is presented. This approach of analysis is based on the use of describing functions technique to obtain quasilinear approximators for the nonlinearities. The quasilinear approximator form and parameters depend on the form and parameters of the input excitation to the system. The describing functions representation is used iteratively in a linear dynamic analysis of the system. This iterative approach can be applied to different types of dynamic analyses employed in the design of piping systems. The iterative method of analysis is presented for the analysis of piping systems with gap and dry friction nonlinearities present in the supports. This method of analysis, which can be integrated into linear elastic analysis programs, is used in a case study of the frequency response analysis of a pipeline model.

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