Free vibrations of free spanning offshore pipelines

Fast and accurate methods for determining pipeline eigenfrequencies and associated bending stresses are essential to free span design, and hence of great interest to the pipeline industry. The Rayleigh–Ritz approach has been applied in combination with a displacement field taken as a Fourier sine series to obtain a novel, semi-analytical solution to an initially curved Euler–Bernoulli beam on a partial elastic foundation subject to axial force. The proposed methodology for calculation of free span eigenfrequencies determines static and harmonic response with excellent accuracy, and includes non-linear geometric effects and the pipe stiffening effect caused by static deformation due to gravity.