In this study, experimental and numerical investigations on the vibration characteristics of a drill pipe during the lowering of a subsea Xmas tree were presented. A fourth-order partial differential equation with variable coefficients was established based on Euler–Bernoulli beam theory. The natural frequencies and mode shapes are obtained by using the differential transformation method. Four drill pipe models of different sizes were used in the experiments which were measured using piezoelectric acceleration sensors and fiber Bragg grating sensors, respectively. The factors that affect the natural frequencies and mode shapes, such as length, diameter, lumped mass, and boundary conditions, were analyzed. The results show that all factors have remarkable effects on the natural frequency, but changes in the length and diameter of the pipe have little effect on the mode shapes; the main factors affecting the mode shape are the boundary conditions and lumped mass. The results of the numerical calculation were validated by a comparison with the experimental results and showed good agreement.
Chaotic oscillations of linear hyperbolic PDE with variable coefficients and implicit boundary conditions
