Modeling of Coriolis mass flow meter of a general plane-shape pipe

The vibration of a general plane tube with a flowing fluid, which is the measuring element in a Coriolis mass flow meter (CMF), is studied. The dynamic stiffness matrix method is used to model such a tube. The tube is divided into straight and circular elements. The elements dynamic stiffness matrices are derived from the equations of motion. By assembling the elements matrices into a global matrix the natural frequencies are obtained. The mode shapes are obtained by applying the boundary conditions at the supports and the compatibility conditions at the nodes. The effects of the flow velocity on the natural frequency and the relative phase difference are modeled. The method is applied to different tube shapes. The results are compared to the published data which reveals good agreement.