Waveguide analysis for ultrasonic medical instruments (comparison of different methods)

Abstract

Transition matrices are derived on the basis of some analytical solutions for a number of waveguides. Initial parameters method is used to analyze the waveguide longitudinal oscillations. This paper contains a comparative analysis of different types of concentrators. The waveguide design scheme presents a straight bar of variable cross-section with different boundary conditions. For given concentrator arrangements, the amplitude axial displacements and longitudinal forces in the ultrasonic medical instrument (UMI) are calculated for a certain excitation frequency. Numerical method for calculation of eigenfrequencies and eigenmodes of the ultrasonic medical instrument (UMI) waveguide is presented. Analysis of the cantilever straight-line concentrator based on the methods of transition matrices and numerical integration by the Runge-Kutta method are under comparison. Sufficient agreement of the results is demonstrated.