Modelling of Ring-Shaped Compound Ultrasonic Waveguides by Means of Finite Elements Method

The paper describes a technique for modelling and optimization of ring-shaped compound ultrasonic waveguides consisting of two sequentially joined segments of different materials by means of finite elements method. The possibility of using such waveguides for amplifying vibrations in amplitude has been justified in the paper. The advantage of the developed technique consists in possibility of its realization by means of standard engineering software, particularly COMSOL Multiphysics. The correctness and efficiency of the technique is proved by comparing the numerical data with the simulation results by means of transfer matrix method using equations of vibration of Euler - Bernoulli and Timoshenko type. It is shown that in compound ring-shaped waveguides two kinds of vibration modes are possible - variable-sign and constant-sign, moreover only constant-sign modes are of practical interest for amplification of vibration amplitude. Recommendations for selection of optimal geometric parameters of the waveguides are given, particularly it is shown that for ensuring maximum vibration amplification factor it is necessary to choose central angles of the waveguide segments with account for calculated dependence between amplification factor and angle, characterized by presence of several local maxima of the amplification factor. It is noted that the high accuracy of the existing semi-analytical methods for calculating and designing ring-shaped waveguides is achieved using methods based on the application of Timoshenko-type equations of vibration.