The plane strain solution is obtained for the natural vibrations and impulse response of a thin circular cylinder containing an added line mass. The solution for a uniform cylinder is derived by taking the added mass to be zero. Numerical calculations of the frequencies and mode shapes for several of the lower modes are presented in graphical form for various values of the added mass. The general impulse response solution for arbitrary initial conditions is obtained by normal mode theory. For both the natural vibrations and impulse response, the theory is found to be in reasonable agreement with available experimental results.

In a particular mode, four distinct solution states are found to exist: a symmetrical and anti-symmetrical branch for each class of vibration, flexural and extensional. Noteworthy features revealed by this investigation are the difference in frequency and mode shape of each solution state and the presence of coupling between the flexural and extensional classes, particularly noticeable in the extensional class mode shapes. In comparing impulse response solutions for velocity with and without the added mass, the major influence of the added mass is found to be an increased participation of the flexural class modes, including the rigid body translation, and decreased participation of the extensional class oscillatory modes.