Study on the Stability of Functionally Graded Simply Supported Fluid-Conveying Microtube under Multi-Physical Fields

The stability of functionally graded simply supported fluid-conveying microtubes under multiple physical fields was studied in this article. The strain energy of the fluid-conveying microtubes was determined based on strain gradient theory, and the governing equation of the functionally graded, simply supported, fluid-conveying microtube was established using Hamilton's principle. The Galerkin method was used to solve the governing equation, and the effects of the dimensionless microscale parameters, temperature difference, and magnetic field intensity on the stability of the microtube were investigated. The results showed that the dimensionless microscale parameters have a significant impact on the stability of the microtube. The smaller the dimensionless microscale parameters were, the stronger the microscale effect of the material and the better the microtube stability became. The increase in the temperature difference decreased the eigenfrequency and critical velocity of the microtube and reduced the microtube stability. However, the magnetic field had the opposite effect. The greater the magnetic field intensity was, the greater the eigenfrequency and critical velocity were, and the more stable the microtube became.