Comments on "On the methods to derive frequency equations of beams carrying multiple masses"
Low [1] used two methods: the frequency determinant method, and the Laplace transform method to obtain the eigenvalues of a clamped-clamped uniform beam carrying two particles in-span. Maple software was used to symbolically evaluate the 12th order frequency determinant into a very lengthy frequency equation. The Laplace transform method is a version of the classical approach to beam vibration problems. Low calculated the ÿrst three eigenvalues of a clamped-clamped beam carrying two particles of the same mass ( 1 = 2 ) and positioned at the same distance from the ends (Á 2 = 1 -Á 1 ), for several combinations of the system parameters by the two methods and tabulated the results to an accuracy of 8 places after the decimal point. One would expect the eigenvalues obtained by the two methods to be identical. Most of the values obtained by the two methods were identical or very nearly identical, but there were some exceptions. The 3rd eigenvalue for the parameters Á 1 = 0:25, 1 = 2 di ered at the 8th place after the decimal point and the 3rd eigenvalue for parameters Á 1 =1=3, 1 = 2 and Á 1 =1=3, 1 = 10 di ered at the 7th place after the decimal point. The di erences are small and may be attributed to computational error. There were three 2nd eigenvalues