Size-dependent Vibration and Instability of Magneto-electro-elastic Nano-scale Pipes Containing an Internal Flow with Slip Boundary Condition

Size-dependent vibrational and instability behavior of fluid-conveying magneto-electro-elastic (MEE)tubular nano-beam subjected to magneto-electric potential and thermal field has been analyzed in thisstudy. Considering the fluid-conveying nanotube as an Euler-Bernoulli beam, fluid-structureinteraction (FSI) equations are derived by using non-classical constitutive relations for MEE materials,Maxwell’s equation, and Hamilton’s principle. Thereafter, taking the non-uniformity of the flowvelocity profile and slip boundary conditions into consideration, modified FSI equation is obtained. Byutilizing Galerkin weighted-residual solution method, the obtained FSI equation is approximatelysolved to investigate eigen-frequencies and consequently instability (critical fluid velocity) of thesystem. In numerical results, a detailed investigation is conducted to elucidate the influences of nanoflowand nano-structure small scale effect, non-uniformity, temperature change, and external magnetoelectricpotential on the vibrational characteristics and stability of the system. This work and theobtained results may be useful to smart control of nano structures and improve their efficiency.