Thermo-mechanical stability of axially graded Rayleigh pipes

Abstract

Thermo-mechanical vibrations of axially functionally graded (AFG) pipes conveying fluid are investigated, aiming at stability enhancement of fluid–interaction systems. Material properties of the pipe vary continuously in the longitudinal direction based on a power-law distribution function. The governing equation of motion of the system was derived using Rayleigh beam theory by considering both linear and nonlinear stress–temperature relations. The Galerkin discretization procedure and eigenvalue analysis were implemented to solve the equation, and stability regions were identified accordingly. The model is validated and compared with the available results in the literature. The influence of material gradient, power index, boundary conditions, rotary inertia factor, temperature rise, and different boundary conditions on the dynamic configuration of the system was elucidated. It was demonstrated that the detached stable regions emerge and develop by increasing the power index at sufficiently high mass ratios. It was shown that either S-shaped or Z-shaped segments may appear on the stability borders. Moreover, the thermal stability map of the supported pipes was also examined, and it was concluded that the AFG power index has a reverse effect on the critical temperature rise of the system at the low and high material gradients. Results of this study may help engineers to design inhomogeneous piping systems optimally.

Communicated by Francesco Tornabene.

Keywords:

• Axially functionally graded pipes
• power gradient index
• thermal stability map
• critical velocity
• rotary inertia factor

Acknowledgement

Iran’s National Science Foundation (INSF) is acknowledged for postdoctoral fellowship granted to Dr. Ali Ebrahimi-Mamaghani (INSF-Grant No. 97009741).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.