The Influence of a Mass on the Free Flexural Vibrations of a Circular Ring. /09RESEARCH and Development Rept

摘要

The general solution is obtained for the free flexural vibrations of a thin circular ring containing a point mass. The solution for a uniform ring alone is derived by taking the point mass to be zero. Numerical calculations of the frequencies of the first and second flexural modes are presented for values of the point mass in the range from zero to infinity. Mode shapes are presented in graphical form. The predominant feature of the investigation is the difference in frequency and mode shape found in the symmetrical and antisymmetrical branches of each mode. It is noted that similar phenomena have been observed experimentally for vibrations of imperfect bodies of revolution. (Author)