Natural frequencies can be obtained from the matrix . Natural frequencies of the simply supported beam are given in Table 12.1. Exact natural frequencies from the analytical closed-form equations and approximate natural frequencies with the finite element method for different number of elements have been tabulated in Table 12.1 for study of the convergence. It is clear that with 10 elements itself the convergence has occurred with reasonable accuracy.

 

Mode no.	Exact	FEM (elements)
		3	6	10	100
I	14.18	14.19	14.18	14.18	14.18
II	56.12	57.39	56.77	56.73	56.72
III	127.6	141.6	128.1	127.7	127.6

Table 12.1: Convergence study of natural frequencies (rad/s)