The influence of a concentrated mass on the free vibrations of a uniform beam

Abstract This paper treats the free vibrations of a uniform beam with elastic end constraints, and with a concentrated mass somewhere along the span. The general frequency equation has been developed as a sixth-order determinant. From this determinant the frequency equations for many important cases have been derived. Curves have been plotted for the first three roots of the frequency equations for six commonly encountered beam systems, for various mass ratios and positions of the concentrated mass.