On nonlinear vibrations of micropipes conveying fluid

This work investigates nonlinear size-dependent resonant characteristics of fluid-conveying extensible micropipes subjected to a harmonic load. The nonlinear governing equation and corresponding boundary conditions of system are developed on the basis of modified couple stress continuum theory in conjunction with Euler-Bernoulli beam theory and von Kármán's geometric nonlinearity. Galerkin technique is employed to discretize the integro-partial-differential governing equation into a set of second-order nonlinear ordinary differential equations with coupled terms. After that, an embedded Runge-Kutta method is utilized to solve numerically the resultant equations. The nonlinear size-dependent primary resonant characteristics of a simply supported micropipe conveying fluid in subcritical domain are examined via depicting frequency-response and force-response curves. The influences of different parameters i.e., flexural rigidity ratio which represent the effect of size-dependency, slenderness ratio, and dimensionless mean flow velocity on the nonlinear size-dependent forced vibration characteristics of system are examined.