Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

Table 4

Error of predicted natural frequencies in experimental cases.

Case	Natural frequency	Theoretical value	PA	FBG	Error1 (%)	Error2 (%)	Error3 (%)
Exp1	1st	10.5147	10.7863	10.3401	2.58	1.66	4.14
	2nd	65.8235	60.4248	63.2812	8.20	3.86	4.73
	3rd	184.2873	174.5605	176.1025	5.28	4.44	0.88
	4th	361.1188	345.4591	345.3308	4.34	4.37	0.04
	5th	596.9475	562.7441	580.5326	5.73	2.75	3.16
	6th	891.7300	825.1953	825.3219	7.46	7.45	0.02
Exp2	1st	6.5076	7.3243	6.2983	12.55	3.22	14.01
	2nd	51.3432	48.8281	50.5211	4.90	1.60	3.47
	3rd	155.5492	151.3672	153.6025	2.69	1.25	1.48
	4th	318.0149	313.1104	312.9178	1.54	1.60	0.06
	5th	539.2983	520.6299	520.6002	3.46	3.47	0.01
	6th	819.4665	800.2637	810.2438	2.34	1.13	1.25
Exp3	1st	5.1823	5.4145	5.0371	4.48	2.80	6.97
	2nd	49.1996	47.6074	47.5933	3.24	3.26	0.03
	3rd	152.8061	150.7568	152.4119	1.34	0.26	1.10
	4th	315.0362	310.3311	311.5492	1.49	1.11	0.39
	5th	536.1817	515.8887	517.5979	3.78	3.47	0.33
	6th	816.2613	788.8086	797.3321	3.36	2.32	1.08
Exp4	1st	4.4392	4.8828	4.1414	9.99	6.71	15.18
	2nd	48.3092	47.6074	47.6291	1.45	1.41	0.05
	3rd	151.7448	149.5361	150.2124	1.46	1.01	0.45
	4th	313.9227	307.0068	310.4764	2.20	1.10	1.13
	5th	535.0382	509.0332	516.1435	4.86	3.53	1.40
	6th	815.0991	787.5117	793.8137	3.38	2.61	0.80
Exp5	1st	3.9487	3.8521	3.8828	2.45	1.67	0.80
	2nd	47.8260	47.6074	47.4852	0.46	0.71	0.26
	3rd	151.1870	147.0947	148.7914	2.71	1.58	1.15
	4th	313.3460	296.6309	307.1457	5.33	1.98	3.54
	5th	534.4506	490.957	515.0786	8.14	3.62	4.91
	6th	814.5047	781.6836	789.8112	4.03	3.03	1.04
Exp6	1st	3.5945	3.6828	3.4392	2.46	4.32	6.61
	2nd	47.5255	46.9971	46.9573	1.11	1.20	0.08
	3rd	150.8466	144.8877	140.8317	3.95	6.64	2.80
	4th	312.9971	294.8539	297.3333	5.80	5.00	0.84
	5th	534.0966	487.3223	513.5267	8.76	3.85	5.38
	6th	814.1477	779.2041	782.8726	4.29	3.84	0.47
Exp7	1st	3.6311	3.9196	3.7399	7.94	3.00	4.58
	2nd	22.6353	24.4731	22.8863	8.12	1.11	6.48
	3rd	63.3445	66.7916	61.7196	5.44	2.57	7.59
	4th	124.1114	118.3987	120.8129	4.60	2.66	2.04
	5th	205.1518	192.9841	197.6397	5.93	3.66	2.41
	6th	306.4508	281.2845	300.1003	8.21	2.07	6.69
Exp8	1st	2.6204	2.8489	2.7537	8.72	5.09	3.34
	2nd	18.4668	19.3654	18.2873	4.87	0.97	5.57
	3rd	54.6145	60.4631	57.3336	10.71	4.98	5.18
	4th	110.6133	116.6287	112.7168	5.44	1.90	3.35
	5th	186.7600	192.7039	189.0539	3.18	1.23	1.89
	6th	283.1069	270.4674	274.4444	4.46	3.06	1.47
Exp9	1st	2.1833	2.3416	2.2396	7.25	2.58	4.36
	2nd	17.5189	18.8431	18.0539	7.56	3.05	4.19
	3rd	53.2767	57.9743	55.8113	8.82	4.76	3.73
	4th	109.0850	112.8	110.3336	3.41	1.14	2.19
	5th	185.1139	189.7431	185.6987	2.50	0.32	2.13
	6th	281.3824	269.1264	273.1249	4.36	2.93	1.49
Exp10	1st	1.9161	2.1341	2.0223	11.38	5.54	5.24
	2nd	17.0886	16.4631	17.2574	3.66	0.99	4.82
	3rd	52.7259	54.7598	53.7434	3.86	1.93	1.86
	4th	108.4875	108.4394	109.2253	0.04	0.68	0.72
	5th	184.4890	183.3648	183.5464	0.61	0.51	0.10
	6th	280.7400	265.153	265.3254	5.55	5.49	0.07
Exp11	1st	1.7319	1.8821	1.7746	8.67	2.46	5.71
	2nd	16.8468	16.1428	16.3394	4.18	3.01	1.22
	3rd	52.4307	51.3689	51.8531	2.03	1.10	0.94
	4th	108.1746	106.2254	107.1038	1.80	0.99	0.83
	5th	184.1660	179.6413	177.6599	2.46	3.53	1.10
	6th	280.4105	261.2791	260.7397	6.82	7.01	0.21
Exp12	1st	1.5955	1.7325	1.7365	8.58	8.83	0.23
	2nd	16.6945	15.9542	15.9987	4.43	4.17	0.28
	3rd	52.2501	49.254	48.4355	5.73	7.30	1.66
	4th	107.9857	103.3634	105.3333	4.28	2.46	1.91
	5th	183.9724	174.9213	176.5189	4.92	4.05	0.91
	6th	280.2139	254.3864	259.2547	9.22	7.48	1.91
Exp13	1st	36.8698	34.4861	6.47%	3.05	3.65	6.47
	2nd	231.0448	223.3359	3.34%	0.50	2.93	3.34
	3rd	646.9281	673.7881	4.15%	0.60	3.41	4.15
	4th	1267.7187	1307.829	3.16%	3.38	0.21	3.16
	5th	2095.6284	2345.238	11.91%	8.86	2.72	11.91
	6th	3130.5047	3380.716	7.99%	5.38	2.42	7.99
Exp14	1st	23.7641	25.9533	22.6144	9.21	4.84	12.87
	2nd	182.1634	192.5408	189.4824	5.70	4.02	1.59
	3rd	548.7162	520.1795	540.8744	5.20	1.43	3.98
	4th	1119.4019	999.7836	1089.3244	10.69	2.69	8.96
	5th	1896.4459	1785.127	1823.8248	5.87	3.83	2.17
	6th	2880.1461	2769.759	2898.0893	3.83	0.62	4.63
Exp15	1st	19.5296	20.2378	18.8513	3.63	3.47	6.85
	2nd	174.6356	187.4995	183.9104	7.37	5.31	1.91
	3rd	538.8244	513.7513	533.0132	4.65	1.08	3.75
	4th	1108.5160	1174.466	1089.7347	5.95	1.69	7.21
	5th	1884.9708	1773.479	1736.2437	5.91	7.89	2.10
	6th	2868.2890	2537.492	2727.3099	11.53	4.92	7.48
Exp16	1st	16.9820	15.713	16.4131	7.47	3.35	4.46
	2nd	171.1710	159.9923	170.0844	6.53	0.63	6.31
	3rd	534.5942	551.7963	547.2145	3.22	2.36	0.83
	4th	1104.0262	1208.198	1137.1944	9.44	3.00	5.88
	5th	1880.3318	1976.187	1901.003	5.10	1.10	3.80
	6th	2863.5560	2761.761	2844.7672	3.55	0.66	3.01
Exp17	1st	15.2184	15.1349	15.2124	0.55	0.04	0.51
	2nd	169.1611	174.3981	177.1978	3.10	4.75	1.61
	3rd	532.2258	530.1284	546.2446	0.39	2.63	3.04
	4th	1101.5536	1194.7641	1116.3345	8.46	1.34	6.56
	5th	1877.7996	1966.9432	1894.1487	4.75	0.87	3.70
	6th	2860.9866	2733.9673	2819.6687	4.44	1.44	3.13
Exp18	1st	13.9106	14.9721	14.1121	7.63	1.45	5.74
	2nd	167.8552	170.9841	172.3347	1.86	2.67	0.79
	3rd	530.7195	526.1192	538.9401	0.87	1.55	2.44
	4th	1099.9959	1181.791	1104.0022	7.44	0.36	6.58
	5th	1876.2124	1951.764	1884.2546	4.03	0.43	3.46
	6th	2859.3811	2710.762	2804.3463	5.20	1.92	3.45
Exp19	1st	12.6734	13.2563	12.3225	4.60	2.77	7.04
	2nd	79.3990	73.7568	78.4572	7.11	1.19	6.37
	3rd	222.3127	220.3311	224.6267	0.89	1.04	1.95
	4th	435.6404	470.4668	452.6511	7.99	3.90	3.79
	5th	720.1421	802.6058	769.3038	11.45	6.83	4.15
	6th	1075.7656	975.1812	1002.0375	9.35	6.85	2.75
Exp20	1st	9.3936	10.0974	9.8236	7.49	4.58	2.71
	2nd	65.5353	66.8899	66.7954	2.07	1.92	0.14
	3rd	192.8674	207.4506	198.1269	7.56	2.73	4.49
	4th	389.6997	450.232	420.3284	15.53	7.86	6.64
	5th	657.1804	600.2085	650.7065	8.67	0.99	8.41
	6th	995.5286	1063.786	987.8547	6.86	0.77	7.14
Exp21	1st	8.0243	7.7562	7.7034	3.34	4.00	0.68
	2nd	62.2993	58.189	60.8146	6.60	2.38	4.51
	3rd	188.1462	200.0332	192.4503	6.32	2.29	3.79
	4th	384.2031	381.5346	390.6624	0.69	1.68	2.39
	5th	651.1935	644.4566	650.8563	1.03	0.05	0.99
	6th	989.2098	1002.723	990.5333	1.37	0.13	1.22
Exp22	1st	7.1245	6.8512	7.3369	3.84	2.98	7.09
	2nd	60.6575	58.2123	57.8555	4.03	4.62	0.61
	3rd	185.9753	195.3257	189.6279	5.03	1.96	2.92
	4th	381.8073	400.4822	395.1465	4.89	3.49	1.33
	5th	648.6642	710.3375	706.5805	9.51	8.93	0.53
	6th	986.5939	1023.985	992.3503	3.79	0.58	3.09
Exp23	1st	6.4695	6.3356	6.4365	2.07	0.51	1.59
	2nd	59.6564	57.3487	57.0213	3.87	4.42	0.57
	3rd	184.7180	188.2234	185.34623	1.90	0.34	1.53
	4th	380.4551	394.8947	388.1113	3.80	2.01	1.72
	5th	647.2570	690.7536	660.2769	6.72	2.01	4.41
	6th	985.1517	1000.325	980.7383	1.54	0.45	1.96
Exp24	1st	5.9677	6.2872	6.1012	5.35	2.24	2.96
	2nd	58.9858	60.7298	56.3343	2.96	4.50	7.24
	3rd	183.9026	188.9128	180.3843	2.72	1.91	4.51
	4th	379.5914	380.9412	377.5567	0.36	0.54	0.89
	5th	646.3656	660.9734	652.2794	2.26	0.91	1.32
	6th	984.2429	991.5867	980.3444	0.75	0.40	1.13