Comparisons of experimental and numerical frequencies for classical beams carrying a mass in-span

A frequency analysis of an Euler-Bernoulli beam carrying a concentrated mas s at an arbitrary location is presented. The dimensionless frequency equati on for ten combinations of classical boundary conditions is obtained by sat isfying the differential equations of motion and by imposing the correspond ing boundary and compatibility conditions. The resulting transcendental fre quency equations are numerically solved. A parametric study on the effects of the mass and its location for each respective case is presented. To veri fy the validity of the transcendental equations, the results for the fixed- fixed cases are compared with those obtained experimentally. On the other h and, approximate results are given, using the Rayleigh's method with two st atic deflection shape functions. The effects of the position and magnitude of the mass, as well as comparisons of the different results obtained analy tically, are investigated and discussed. The comparisons clearly show that the eigenfrequencies of the beam-mass system can be accurately predicted by solving the transcendental equation, whereas the closed-form Rayleigh's ex pression is suggested for a quick estimation of fundamental frequency. (C) 1999 Elsevier Science Ltd. All rights reserved.