Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory

In this paper, size dependent stability analysis of cantilever micro-pipes conveying fluid is investigated. The mathematical derivations are expanded in terms of three length scale parameters using the modified strain gradient theory (MSGT) in conjunction with the Euler–Bernoulli beam model. The MSGT encompasses modified couple stress theory (MCST) and classical theory (CT) when two of three length scale parameters or all of them are taken to be zero, respectively. The size dependent governing equation and associated boundary conditions are derived by applying extended Hamilton's principle and are discretized through the extended Galerkin method. An eigen analysis is performed and a parametric study is then carried out to examine the effect of length scale parameter, outside diameter and aspect ratio on the natural frequencies and the flutter critical speeds. Results affirm that MSGT predicts greater natural frequencies and more flutter critical speeds than that predicted by MCST and CT.