Bounds to Bending Frequencies and Mode Shape Estimates for Free Nonuniform Beams with Attached Masses. Part I: Analysis and Results.
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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The report presents procedures for computing upper and lower bounds to bending frequencies and estimates of mode shapes of beams with piecewise constant stiffness and mass and with elastically attached masses. The Rayleigh-Ritz procedure was used to obtain the upper bounds and the mode shapes lower bounds were obtained using the method of Intermediate Problems. Several features of these methods are that they give upper and lower bounds that bracket the true frequencies they are computationally fast, accurate, and easy to use they can handle beams with a large number of stiffness and mass variations and many elastically attached masses and they yield improvable bounds, i.e., as the sizes of the matrices used in the numerical computations are increased, the upper and lower bounds converge to the true frequencies. Author
- Structural Engineering and Building Technology