Three-Dimensional Theory of Longitudinal-Radial Coupled Vibration for Annular Elastic Cylinder

摘要

In this paper, the resonance frequencies of longitudinal-radial coupled vibration, and the relationships between the resonance frequencies and the dimensions of the cylinders with comparable longitudinal and radial dimensions are studied. Based on elastic dynamic equation and according to the boundary conditions of free-end annular elastic cylinder, the resonance frequency equation of annular cylinder of longitudinal-radial coupled vibration is derived. The first two order resonance frequencies are calculated by using MATLAB software and their vibrational distributions are simulated by using ANSYS software. The results show that the analytical resonance frequencies are in good agreement with the numerical results. Besides, compared with the analytical, numerical or experimental results in references [1] and [2], it can be also seen that the present theory is suitable for not only annular cylinders but also solid cylinders. So, it is expected that this theory can serve as reference for the design of the longitudinal-radial composite vibrational systems.