Transverse Vibration of Nonuniform, Internally Damped Cantilever Beams.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK ORDNANCE RESEARCH LAB
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The Bernoulli-Euler theory of transverse beam vibration, suitably extended to take into account internal damping, is used to derive general expressions in closed-form for the driving-point impedance and force transmissibility of each of three types of nonuniform cantilever beam a truncated beam of rectangular section with constant breadth and a depth of increasing or decreasing linear taper, a truncated beam of rectangular section with a depth of increasing or decreasing linear taper and a breadth appropriately varied hyperbolically to maintain constant cross-sectional area, and a beam composed of three stages, each of which is uniform but varies arbitrarily from the others in cross section and length. In each case, the beam is driven at its free end by a sinusoidally varying point force, and the frequency dependence of its impedance and transmissibility has been calculated. Representative results are presented for beams having the same length and mass and are compared with the response of an equally long and massive uniform beam. Author
- Marine Engineering