On the methods to derive frequency equations of beams carrying multiple masses

Two commonly used methods to generate the eigenfrequency equation of a beam carrying multiple concentrated masses at an arbitrary location are of main concern in this paper. Both the methods of frequency determinant and the m ethod of Laplace transform are considered and compared here for the effecti veness of each derivation for the frequency equation of the same system. Th e dimensionless frequency equation for a clamped-clamped beam carrying two different masses is obtained for comparison. The computational times to gen erate the same expression by using the two methods are noted. It is found t hat the processing and computational time by using the Laplace transform is longer although the resultant system equations are often claimed to be mor e compact than those by the method of frequency determinant. (C) 2000 Elsev ier Science Ltd. All rights reserved.