Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 54 8 2022 10 23 Vibration and Stability Analysis of Micro-pipes Conveying Fluid under Magnetic, Electric, and Thermal Fields Vibration and Stability Analysis of Micro-pipes Conveying Fluid under Magnetic, Electric, and Thermal Fields 1803 1832 4884 10.22060/mej.2019.15800.6205 FA Mohammad Hosseini Department of Mechanical Engineering, Sirjan University of Technology Afshin Hosseini Department of Mechanical Engineering, Sirjan University of Technology Reza Bahaadini Department of Mechanical Engineering, Shaid Bahonar University of Kerman, Kerman, Iran Journal Article 2019 02 09 In this study, vibration and stability analysis of micro-pipes conveying fluid under magnetic, electric, and thermal fields using classical, modified coupled stress, and modified strain gradient theories are presented. The Euler-Bernoulli beam theory with clamped-pinned, clamped-clamped, and pinned-pinned boundary conditions is used for modeling the pipe. The differential equations governing the vibration of conveying fluid micro-pipe are derived through extended Hamilton’s method. Additionally, the extended Galerkin’s method is used to convert the governing partial differential equations into ordinary differential equations. The effects of size, boundary conditions, magnetic field, electric field, and thermal field on eigenvalues and critical velocity are investigated. The results indicated that the strain gradient theory predicts the highest natural frequencies and critical fluid velocities among the other two theories. The effects of magnetic, electric, and thermal fields along with different boundary conditions on eigenvalues and critical fluid velocity have been studied. It has also been concluded that the impact of these fields on the stability regions is different for different boundary conditions. Furthermore, the results showed that the stability of the micro-pipes increases with the increase of the magnetic field coefficient, but decreases with the increase of the coefficient of electric and thermal fields. In this study, vibration and stability analysis of micro-pipes conveying fluid under magnetic, electric, and thermal fields using classical, modified coupled stress, and modified strain gradient theories are presented. The Euler-Bernoulli beam theory with clamped-pinned, clamped-clamped, and pinned-pinned boundary conditions is used for modeling the pipe. The differential equations governing the vibration of conveying fluid micro-pipe are derived through extended Hamilton’s method. Additionally, the extended Galerkin’s method is used to convert the governing partial differential equations into ordinary differential equations. The effects of size, boundary conditions, magnetic field, electric field, and thermal field on eigenvalues and critical velocity are investigated. The results indicated that the strain gradient theory predicts the highest natural frequencies and critical fluid velocities among the other two theories. The effects of magnetic, electric, and thermal fields along with different boundary conditions on eigenvalues and critical fluid velocity have been studied. It has also been concluded that the impact of these fields on the stability regions is different for different boundary conditions. Furthermore, the results showed that the stability of the micro-pipes increases with the increase of the magnetic field coefficient, but decreases with the increase of the coefficient of electric and thermal fields. https://mej.aut.ac.ir/article_4884_c133fb1bb634af68c5088f3438848bfd.pdf