A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses
The author presents a frequency analysis for Euler-Bernoulli beams carring multiple masses with different boundary conditions. The location of concentrated masses on a uniform beam is arbitrary. The exact frequency equations for classical boundary conditions (fixed, free, pinned, guided ends) are derived by using differential equations and boundary and compatibility conditions of the corresponding eigenvalue problems. Then the author derives the frequency equation in ``determinant'' form by the application of Maple. The main purpose is to investigate the validity of Dunkerley formula for uniform Euler-Bernoulli beams carring multiple masses. The author discuss a modification of Dunkerley formula, and the results obtained by the modified Dunkerley formula are compared to those obtained from the ``exact'' frequency equations. An error parameter is introduced to characterize the efficiency of Dunkerley's formula. The author establishes that the modified Dunkerley expression can generally yield good approximation of natural frequencies. The computational time saved due to Dunkerley method is illustrated by several examples.
scientific article; zbMATH DE number 1488703