Influence of boundary conditions on Coriolis flow meter measurement

A Coriolis flowmeter can be described by one-dimensional differential equations with appropriate boundary conditions (e.g. Bernoulli's beam theory for bending). As the dependence of the properties of the eigenmodes from the boundary conditions is critical for the performance of a flowmeter, its understanding is important for the development of better devices. In this paper we study how changes in the boundary conditions of ordinary differential equations can be treated with perturbation theory. We describe three perturbative theories allowing to predict effects of boundary perturbation: (i) a direct series expansion using boundary integrals, (ii) a series expansion in the boundary conditions, and (iii) an expansion in the old eigenfunctions. As the described methods are completely general, their application in similar fields is possible.