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

Table 1

Comparison of the first three dimensionless natural frequencies of rotating solid tapered Euler-Bernoulli beams at , , , .

Present	Ref. [14]	Present	Ref. [14]	Present	Ref. [14]	Present	Ref. [14]	Present
0		3.5164	3.5160	3.9570	3.9567	4.6257	4.6252	5.8293	5.8231	8.7445
		22.0366	22.0345	20.8091	20.807	19.5514	19.5476	18.5183	18.480	20.1042
		61.6960	61.6972	55.3500	55.3304	48.5953	48.5789	41.4611	41.321	36.5279
5		6.4499	6.4495	6.7732	6.7729	7.2905	7.2901	8.2653	8.2620	10.6634
		25.4483	25.4461	24.0673	24.0660	22.6379	22.6360	21.4209	21.384	22.8601
		65.2118	65.2050	58.6518	58.6364	51.7012	51.6918	44.4176	44.269	41.0619
10		11.2029	11.2023	11.4859	11.4856	11.9419	11.9415	12.7928	12.791	14.7477
		33.6417	33.6404	31.8863	31.8895	30.0289	30.0299	28.3381	28.301	29.4213
		74.6671	74.6493	67.5293	67.5316	60.0369	60.0399	52.2738	52.100	51.2478
15		16.1445	-	16.4165	-	16.8587	-	17.6745	-	19.4476
		43.9323	-	41.7005	-	39.2756	-	36.9308	-	37.5106
		87.9543	-	80.0153	-	71.7371	-	63.1548	-	59.9363