On nonlinear vibrations of micropipes conveying fluid

Abstract

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.