Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid

Abstract

A Meshfree Radial Basis Collocation Method (RBCM) associated with explicit and implicit time integration scheme is formulated to study the coupling dynamics of a rotating flexible tube conveying fluid, which involves a partial differential equation (PDE) with variable coefficients. Dispersion studies are performed and they indicate that the proposed RBCM has a very small dispersion error compared with conventional FEM and Galerkin-based meshfree methods. Numerical examples are conducted for the influence of initial flow rate of the fluid, discretization and shape parameter on the dispersion error. The critical time step is obtained from a Von Neumann stability analysis. For the eigenproblem, Hermite-type RBCM is proposed in order to construct square matrices and eigenvalue analysis gives the frequencies of the system. Subsequently, the influence of angular velocity, flow rate of the fluid and the time variation on the fundamental frequencies is studied. Though proposed for studying the dynamics of a rotating flexible tube conveying fluid, this solution scheme is applicable to other dynamical problems which have similar PDEs with variable coefficients.