Abstract
Natural frequencies and modes are determined for beams having a continuous mass distribution as well as a finite number of concentrated masses with rotary inertia. The method also includes the effects of discrete elastic supports and torsional restraints. Solutions are obtained by expanding the time dependent deflection curve in terms of well known characteristic beam functions and then solving a set of linear equations for eigenfrequencies and modes. Solutions for a simple beam having a torsional end restraint and a cantilever beam with a concentrated end mass and stiffness are obtained in order to illustrate the method.
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