NON LINEAR VIBRATIONS OF A STRAIGHT PIPE WITH NON LINEAR BOUNDARY CONDITIONS.
A new non-linear model of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler–Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton’s principle the coupled non-linear equations of motion for the longitudinal and transverse displacements are derived. These equations of motion are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the generalized- α time integration method to the non-linear discretized equations. The validity of the new modelling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by Paı̈doussis
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