Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section

Table 6

The first three-order dimensionless natural frequencies of rotating tapered hollow beams for various ratios of hub radius to beam length  .

0		4.0021	4.0021	4.0021	4.0743	4.0743	4.0743
		19.1933	19.1933	19.1933	21.1137	21.1137	21.1137
		45.1361	45.1361	45.1361	55.0759	55.0759	55.0759
5		6.9391	7.9790	9.1094	7.1163	8.1648	9.3065
		22.2340	23.5717	25.1345	24.6043	26.0908	27.8311
		47.8600	49.1793	50.7682	58.5679	60.2042	62.1795
10		11.8553	14.1905	16.6439	12.1676	14.5191	16.9959
		29.4809	29.4809	37.4245	32.8996	37.1390	41.7938
		55.0961	59.0961	64.2301	67.8847	73.2615	79.3845
15		17.0078	20.6152	24.3667	17.4498	21.0838	24.8719
		38.5013	44.7447	51.3531	43.2329	50.2622	57.7703
		65.0693	72.6549	80.8113	80.8610	90.5387	101.1210