Browsing by Author "Palmer, Edward Wilkerson"

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    The influence of a mass on the free flexural vibrations of a circular ring
    Palmer, Edward Wilkerson (Virginia Polytechnic Institute, 1962)
    The general solution was obtained for the free flexural vibrations in the plane of a thin circular ring containing a point mass. As a degenerate case of the general solution, the solution for a uniform ring alone was derived from the general solution by taking the point mass to be zero. Numerical calculations of the frequencies and mode shapes of the first and second flexural modes were made for values of the point mass in the range from zero to infinity. The results are presented in graphical form. The predominant feature of the investigation was the difference in frequency and mode shape found in the symmetrical and antisymmetrical modes, and the particular orientation of the nodes with respect to the point mass. It was noted that similar phenomena were observed experimentally for vibrations of imperfect bodies of revolution. In conclusion, it was brought out that a ring with a point mass offers a convenient mathematical model for a preliminary theoretical investigation of the vibrations of imperfect bodies of revolution.
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    The influence of added mass on the natural vibrations and impulse response of long, thin cylindrical shells
    Palmer, Edward Wilkerson (Virginia Polytechnic Institute and State University, 1970)
    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.