Abstract
To enhance the safety and stability of Ocean Thermal Energy Conversion (OTEC) processes, non-uniform and variable cross-section cold-water pipes (CWPs) are used. These pipes exhibit complex and intriguing vibration phenomena in hash marine environments. This paper presents a novel mathematical model to study the stability of vibrations in non-uniform and variable cross-section pipes caused by internal flows. Based on the Euler-Bernoulli beam theory, a new control equation for the vibrations of non-uniform and variable cross-section pipes is established. Initially, the Generalized Integral Transform Technique (GITT) is employed to separate variables, followed by the SLEUTH method (Sturm-Liouville Eigenvalues Using Theta matrices) to obtain the eigenvalues and eigenfunctions in discrete forms. Finally, the GITT method is applied to solve the newly derived control equation. The mathematical model has been validated against published data for convergence and accuracy. Numerical results indicate that with linear and parabolic changes in cross-section, as well as polynomial and trigonometric changes in flexural stiffness and density, the mass ratio and gravity parameters significantly affect the critical flow velocity, frequency, and modal shapes. Our research method can be applied to design non-uniform and variable cross-section CWPs for specific marine conditions.