On nonlinear stability of fluid-conveying imperfect micropipes

Micropipe conveying fluid as a core element can be found in many microfluidic devices. In such scale, size effect phenomenon in micropipe may play a significant role in the mechanical behavior of system. In addition, due to the improper production process, the micropipe may be fabricated with a geometric imperfection. Hence, this study objects to investigation of the size-dependent and -independent stability behavior of geometrically perfect and imperfect extensible micropipe conveying fluid under different boundary conditions. In the framework of modified couple stress theory, the nonlinear equations of system are established based on Euler-Bernoulli beam theory. Statics-based analytical solutions are developed to study the nonlinear stability characteristics of system. The statics-based results are verified by aid of a dynamics-based numerical solution. It is indicated that for a perfect case the system becomes unstable at a critical velocity via a pitchfork bifurcation. But, for an imperfect case the system may lose its stability at a primary critical velocity by a perturbed pitchfork bifurcation also it becomes unstable at a secondary critical velocity by a transcritical bifurcation. It is found that the primary and secondary critical velocities of the imperfect case are, respectively, smaller and greater than the critical velocity of the perfect case. A parametric study is conducted to highlight the influence of different dimensionless parameter as well as boundary conditions on the nonlinear stability behavior of system. Finally, it should be pointed out that the analytical solution and the presented results not only for the size-dependent pipe conveying fluid in micro scale but also for the size-independent pipe conveying fluid from macro to micro scale can be utilized.