FREE-VIBRATION ANALYSIS OF A UNIFORM CANTILEVER BEAM WITH POINT MASSES BY AN ANALYTICAL-AND-NUMERICAL-COMBINED METHOD

The natural frequencies and mode shapes of a uniform cantilever beam carrying any number of concentrated masses were determined by using an analytical-and-numerical-combined method (ANC method). The eigenvalue equation was first derived analytically by using the expansion theorem and then the eigenvalues and eigenvectors were calculated numerically. In comparison with the general finite element method (FEM), the ANC method has the advantage that there is no necessity to derive the property matrices of each beam element and then to develop the overall ones of the entire beam. In comparison with the transfer matrix method (TMM) the ANC method requires no tedious matrix multiplication so that some computer time may be saved. The ANC method is also better than the pure analytical (closed form) method, since, instead of a few special cases, a uniform beam carrying any number of point masses of various magnitudes or distributions along the beam length can be easily solved. Besides, by using the ANC method, there is no difficulty in taking more modes in the mode superposition equation and hence more higher mode natural frequencies of better accuracy may be obtained. © 1990.