Frequency Equations for the In-Plane Vibration of Circular Annular Disks

Table 9

Frequency parameters of in-plane vibration of an annular disk with flexible boundary conditions.

Boundary conditions	𝑛=1		𝑛=2		𝑛=3		𝑛=4
	Reference [19]	present study	Reference [19]	present study	Reference [19]	present study	Reference [19]	present study
Elastic-Free	0.771	0.771	1.408	1.408	2.121	2.121	2.772	2.772
	1.906	1.906	2.524	2.524	3.444	3.444	4.397	4.397
Elastic-Clamped	2.590	2.590	3.117	3.116	3.928	3.926	4.759	4.760
	3.625	3.625	4.134	4.136	5.000	5.001	5.957	5.957
Elastic-Elastic	1.494	1.492	1.815	1.813	2.474	2.472	3.123	3.120
	2.603	2.601	3.209	3.207	4.004	4.002	4.859	4.857
Free-Elastic	1.040	1.046	1.505	1.504	2.414	2.416	3.114	3.116
	2.432	2.432	3.018	3.018	3.895	3.896	4.833	4.834
Clamped-Elastic	1.686	1.686	1.960	1.959	2.514	2.512	3.129	3.127
	2.764	2.765	3.319	3.317	4.061	4.060	4.879	4.877