Vibration analysis of buried pipelines and piles using differential transformation method

Investigating the interaction between structures and their elastic foundations is essential in structures with elastic support conditions, such as buried pipelines and piles. Research investigation was carried out to find the frequency of a buried structure simulated by Euler–Bernoulli beam equations, with distributed damping and general boundary conditions on an elastic foundation. The elastic bed was modelled by a linear spring, and boundary conditions were changeable at two ends of the beam's support with variations in the stiffness of transitional and rotational springs. The differential transformation method (DTM) was then used to solve the equations by correlating the function and its derivatives. The frequency of the structure was obtained for various damping and stiffness values. The increase in the stiffness of the elastic support and the decrease in damping led to a higher frequency. The results of DTM agreed with the results of the exact method.