Establishment of Mathematical Model of Buried Pipeline on Nonlinear Soil Dynamic Model

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper, the supported form of pin rocker bearing in the analysis of transverse vibration. Kelvin viscoelastic foundation model is adopted and the dynamic model of soil spring is regarded as nonlinearity. Applying the principle of Hamilton, the differential equation of vibration is deduced. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equations are discreted and transformed into state formulas. The critical flow velocity is obtained using the Matlab software in a typical numerical example.

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