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 method of Laplace transform are considered and compared here for the effectiveness of each derivation for the frequency equation of the same system. The dimensionless frequency equation for a clamped–clamped beam carrying two different masses is obtained for comparison. The computational times to generate the same expression by using the two methods are noted. It is found that the processing and computational time by using the Laplace transform is longer although the resultant system equations are often claimed to be more compact than those by the method of frequency determinant.