Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

Table 11

Nondimensional natural transverse frequencies for axially FG tapered beam with respect to taper ratio , .

		P-P					C-C
Case  1		0	11.4560	45.6887	102.6601	182.4345	285.1358	24.0660	68.1328	135.4215	225.7493	339.2851
	0.2	10.2635	41.0849	92.2393	163.8387	256.0119	21.5207	61.0451	121.4017	202.4339	304.2973
	0.4	8.8941	36.2851	81.2897	144.1972	225.1632	18.8852	53.6029	106.6116	177.8075	267.3534
	0.6	7.2513	31.1822	69.5172	122.9219	191.6076	16.1104	45.6006	90.5999	151.0965	227.2883
	0.8	5.0932	25.5025	56.1391	98.3922	152.5382	13.0533	36.4076	71.8833	119.5672	179.6797
Case  2	0	9.9366	40.0700	90.5367	161.3146	252.4647	24.8068	66.2401	127.6871	209.1345	310.8793
	0.2	8.8494	35.9365	81.2126	144.6952	226.4368	22.3802	59.6013	114.7530	187.8207	279.0755
	0.4	7.6207	31.6402	71.4122	127.1143	198.8076	19.8231	52.5571	100.9830	165.0931	245.1303
	0.6	6.1724	27.0932	60.8831	108.0671	168.7522	17.0641	44.8967	85.9592	140.2721	208.0589
	0.8	4.3128	22.1136	49.1297	86.6404	134.9467	14.0097	36.3471	69.2653	113.0049	167.9583
		C-P					C-F
Case  1	0	16.4111	54.9276	116.4430	201.0000	308.7099	3.5340	23.7075	68.1642	135.4187	225.7516
	0.2	15.3662	49.9039	105.0941	180.9523	277.5884	3.9253	22.6573	62.5140	122.8555	203.8977
	0.4	14.2204	44.6316	93.1433	159.8062	244.7549	4.4598	21.5947	56.6601	109.7005	180.9238
	0.6	12.9302	38.9644	80.2439	136.9256	209.2062	5.2495	20.5907	50.5440	95.6707	156.2332
	0.8	11.3909	32.4806	65.3274	110.2051	167.3687	6.5769	19.9787	44.1206	79.9627	127.8152
Case  2	0	17.3037	53.9917	110.4619	186.8845	283.5206	4.1801	24.4362	66.2609	127.6897	209.1407
	0.2	16.2634	49.2161	99.9160	168.4860	255.1649	4.5112	23.3314	60.8734	116.0144	189.0897
	0.4	15.1061	44.1433	88.7009	148.8877	224.9241	4.9675	22.1766	55.2115	103.6541	167.7838
	0.6	13.7727	38.6134	76.4763	127.5011	191.9048	5.6563	21.0079	49.1851	90.3173	144.6597
	0.8	12.1299	32.2583	62.5395	103.3128	154.9786	6.8715	20.0744	42.7624	75.5952	118.9682