Natural frequency and critical velocities of heated inclined pinned PP-R pipe conveying fluid

Purpose: The flow velocity and pressure of fluid flowing through a pipeline can cause the vibration of pipes, and consequently result in the modification in natural frequency via fluid-structure interaction. The value of the natural frequency of a component when approaches the excitation force to a certain degree, a severe resonance failure may occur. Hence, avoiding the resonance failure of a pipe subjected to complex conditions is an essential issue that requires to be solved urgently in the engineering field. This work treats the transverse vibration for flexible inclined heated pipe, made of polypropylene randomcopolymer (PP-R), conveying fluid assuming pinned connections at the ends. The pipe was placed at different support angles and subjected to variant temperatures. Design/methodology/approach: The inclined pipe is modelled as Euler-Bernoulli beam taking into account its self-weight, temperature variation, inclination angle, aspect ratio, and internal fluid velocity. The integral transforms method, which includes the finite Fourier sine and the Laplace transforms, was used to develop an analytic solution to the modified equation of motion and the analytical expressions for dual natural frequencies of the pipefluid interaction system were computed. Findings: The proposed solution technique via finite Fourier sine and Laplace transforms offers a more convenient alternative to calculate the dynamic characteristic of pipes conveying fluid. The obtained results showed that the dynamical behaviour of pipe–fluid system is strongly affected by fluid flow velocity, degree of inclination, temperature variation, and aspect ratio of the pipe in transverse modes. Research limitations/implications: This work focuses on fundamental (first) mode in the most discussions. Practical implications: It was revealed that the thermal effects in the pipe are a very important factor and more significant in comparison with the internal fluid velocity and the inclination angle has a larger impact on vibration characteristics at a higher aspect ratio. The findings can be useful for the design of engineering components. Originality/value: Determining the combining effect of inclination angle, aspect ratio, and thermal loading on vibration characteristic of the pipes conveying fluid by using an improved analytic solution to the modified equation of motion via mixed of finite Fourier sine and Laplace transforms.