Dynamic boundary characteristics for truncated model of V-shaped orthogonally stiffened plates

参数	数值
弹性模量E/Pa	2.1×10¹¹
密度ρ/(kg·m⁻³)	7 800
泊松比v	0.3
主板厚度h/m	0.01
主板长度L_x/m	1.00
主板宽度L_y/m	1.00
附板厚度h₁/m	0.01
附板长度L/m	0.70
加强筋高度H/m	0.02
加强筋宽度B/m	0.01
V形板夹角的补角α/（°）	60

Table 2. Natural frequencies and their maximum differences of V-shaped connecting plates under different grid sizes

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Table 2. Natural frequencies and their maximum differences of V-shaped connecting plates under different grid sizes

网格属性		不同阶数(m, n)的固有频率				最大差值/%
尺寸/m	网格数量	(1, 1)	(2, 2)	(3, 3)	(4, 4)	最大差值/%
0.010	17 924	127.07	341.98	625.64	1 042.46	—
0.009	22 516	127.04	341.89	625.36	1 041.82	0.061
0.008	28 360	127.02	341.81	625.14	1 041.31	0.049
0.007	36 427	127.00	341.73	624.94	1 040.83	0.046
0.006	49 933	126.98	341.66	624.74	1 040.42	0.041
0.005	71 422	126.95	341.59	624.57	1 040.03	0.036
0.004	110 299	126.94	341.54	624.43	1 039.71	0.032
0.003	197 003	126.93	341.50	624.32	1 039.51	0.019
0.002	433 856	126.92	341.47	624.27	1 039.34	0.019

Table 3. Comparison between the results of this article and those of Reference [5]
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Table 3. Comparison between the results of this article and those of Reference [5]
模态阶数文献[5]固有频率/Hz 本文固有频率/Hz 误差/%
1 24.24 24.29 0.21
2 30.88 30.84 0.13
3 61.25 61.07 0.29
4 69.25 69.26 0.01
5 117.46 117.27 0.16

Table 4. The (m, n)-order natural frequencies f and their variation rate κ₁ of V-shaped plates under different coupling angles α

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Table 4. The (m, n)-order natural frequencies f and their variation rate κ₁ of V-shaped plates under different coupling angles α

α/(°)	(1, 1)		(1, 2)		(2, 1)		(2, 2)		(3, 3)		(4, 4)
α/(°)	f/Hz	κ₁	f/Hz	κ₁	f/Hz	κ₁	f/Hz	κ₁	f/Hz	κ₁	f/Hz	κ₁
0	97.09	—	198.63	—	196.69	—	307.53	—	531.24	—	934.07	—
3	109.20	4.04	200.55	0.64	205.07	2.79	309.49	0.65	536.77	1.84	944.82	3.58
6	119.96	3.59	207.28	2.24	218.48	4.47	315.73	2.08	554.57	5.93	954.14	3.11
9	123.94	1.33	216.73	3.15	224.28	1.93	323.97	2.75	580.85	8.76	973.66	6.51
12	125.36	0.47	223.26	2.18	226.45	0.72	329.93	1.99	608.80	9.32	996.29	7.54
15	125.99	0.21	226.85	1.20	227.43	0.33	333.37	1.15	621.25	4.15	1 013.80	5.84
18	126.33	0.11	228.89	0.68	227.94	0.17	335.35	0.66	623.38	0.71	1 024.10	3.43
20	126.47	0.07	229.77	0.44	228.15	0.11	336.20	0.42	624.09	0.36	1 028.00	1.95
30	126.78	0.03	231.86	0.21	228.63	0.05	337.92	0.17	622.84	0.13	1 036.20	0.82
40	126.87	0.01	232.58	0.07	228.77	0.01	340.89	0.30	622.85	0	1 038.00	0.18
50	126.89	0	232.90	0.03	228.82	0	341.19	0.03	622.77	0.01	1 038.70	0.07
60	126.88	0	233.07	0.02	228.84	0	340.89	0.03	622.67	0.01	1 039.00	0.03
70	126.87	0	233.16	0.01	228.84	0	340.82	0.01	622.58	0.01	1 039.20	0.02
80	126.86	0	233.22	0.01	228.84	0	340.79	0	622.48	0.01	1 039.20	0
90	126.84	0	233.26	0	228.84	0	340.77	0	622.38	0.01	1 039.20	0

Table 5. The (m, n)-order natural frequencies f and their variation rate κ₂ of V-shaped plates under different thickness of the attached plate

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Table 5. The (m, n)-order natural frequencies f and their variation rate κ₂ of V-shaped plates under different thickness of the attached plate

附板厚度h₁/mm	(1, n)		(2, n)		(3, n)		(4, n)
附板厚度h₁/mm	f/Hz	κ₂	f/Hz	κ₂	f/Hz	κ₂	f/Hz	κ₂
3	72.53	—	211.34	—	472.06	—	1 025.90	—
4	96.07	23.54	225.06	13.72	473.39	1.33	1 026.90	1.00
5	117.06	20.99	249.87	24.81	473.84	0.45	1 031.00	4.10
6	122.52	5.46	295.97	46.10	514.40	40.56	1 033.10	2.10
7	124.39	1.87	328.89	32.92	592.86	78.46	1 033.20	0
8	126.30	1.91	334.77	5.88	626.96	34.10	1 055.00	21.90
9	128.84	2.54	338.86	4.09	633.21	6.25	1 159.70	104.70
10	134.02	5.18	347.35	8.49	640.51	7.30	1 260.30	100.60
11	143.25	9.23	370.72	23.37	701.86	61.35	1 280.90	20.60
12	153.86	10.61	399.81	29.09	758.24	56.38	1 289.70	8.80
13	164.78	10.92	429.36	29.55	812.71	54.47	1 333.10	43.40
14	175.77	10.99	457.78	28.42	842.75	30.04	1 423.90	90.80
15	186.76	10.99	479.71	21.93	850.94	8.19	1 514.70	90.80
16	197.67	10.91	487.62	7.91	852.42	1.48	1 582.70	68.00
17	208.41	10.74	490.35	2.73	856.33	3.91	1 598.00	15.30
18	218.75	10.34	492.12	1.77	864.79	8.46	1 601.60	3.60
19	227.97	9.22	492.30	0.18	896.43	31.64	1 604.90	3.30
20	234.44	6.47	493.55	1.25	938.28	41.85	1 620.20	15.30
21	237.64	3.20	494.64	1.09	981.06	42.78	1 684.20	64.00
22	239.20	1.56	496.71	2.07	1 023.40	42.34	1 755.70	71.50
23	240.13	0.93	506.25	9.54	1 065.70	42.30	1 827.10	71.40
24	240.76	0.63	526.59	20.34	1 117.10	51.40	1 894.20	67.10
25	241.23	0.47	545.88	19.29	1 157.60	40.50	1 913.00	18.80

Table 6. The (m, n)-order natural frequencies f and their variation rate κ₃ of V-shaped plates under different length of the attached plate

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Table 6. The (m, n)-order natural frequencies f and their variation rate κ₃ of V-shaped plates under different length of the attached plate

附板长度L/cm	(1, n)		(2, n)		(3, n)		(4, n)
附板长度L/cm	f/Hz	κ₃	f/Hz	κ₃	f/Hz	κ₃	f/Hz	κ₃
35	355.06	—	478.88	—	852.35	—	1 279.90	—
40	346.92	3.39	471.52	1.47	842.12	2.05	1 275.40	0.90
45	321.99	4.88	442.05	6.63	842.20	0.03	1 250.40	5.70
48	299.95	7.35	415.87	8.73	834.58	2.54	1 182.00	22.80
50	288.24	5.85	401.63	7.12	834.72	0.07	1 148.40	16.80
53	270.02	6.07	379.64	7.33	825.28	3.15	1 086.99	20.47
55	261.00	4.51	369.01	5.31	818.10	3.59	1 065.40	10.79
57	251.95	4.53	357.97	5.52	788.94	4.96	1 051.20	7.10
60	243.83	2.71	348.87	3.03	759.79	16.13	1 044.00	2.40
65	236.46	1.47	341.87	1.40	700.41	11.88	1 041.60	0.48
70	233.37	0.62	341.47	0.08	655.79	8.92	1 039.70	0.38
75	231.58	0.36	339.30	0.43	602.42	10.67	1 032.70	1.40
80	230.21	0.27	338.23	0.21	573.75	5.73	1 001.40	6.26
85	228.82	0.28	337.22	0.20	546.49	5.45	950.57	10.17
90	227.04	0.36	335.86	0.27	523.45	4.61	909.66	8.18
95	224.16	0.58	333.34	0.50	503.86	3.92	873.08	7.32
100	218.81	1.07	327.42	1.18	489.20	2.93	850.25	4.57
110	200.82	1.80	305.80	2.16	480.52	0.87	777.60	7.26
120	182.54	1.83	284.76	2.10	479.50	0.10	735.27	4.23
130	167.10	1.54	267.53	1.72	477.33	0.22	703.74	3.15
140	154.45	1.27	252.66	1.49	474.56	0.28	689.48	1.43
150	144.32	1.01	243.05	0.96	459.50	1.51	682.11	0.74

Table 7. The natural frequency f and their variation rate κ₄ of isolated plate under different elastic support stiffness

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Table 7. The natural frequency f and their variation rate κ₄ of isolated plate under different elastic support stiffness

lg(k/k₀)	(1, n)		(2, n)		(3, n)		(4, n)
lg(k/k₀)	f/Hz	κ₄	f/Hz	κ₄	f/Hz	κ₄	f/Hz	κ₄
0	155.61	—	383.27	—	688.23	—	1 121.40	—
1.000 0	155.96	0.35	383.63	0.36	688.57	0.34	1 121.70	0.30
2.000 0	159.14	3.18	386.99	3.36	691.89	3.32	1 125.10	3.40
2.397 9	163.72	11.51	391.96	12.49	696.99	12.82	1 130.30	13.07
2.699 0	169.85	20.36	398.93	23.15	704.48	24.88	1 137.90	25.24
3.000 0	179.82	33.12	409.74	35.91	716.78	40.86	1 150.40	41.53
3.310 3	192.33	40.32	424.62	47.95	734.32	56.53	1 168.70	58.98
3.602 1	205.91	46.54	441.86	59.08	758.97	84.48	1 191.90	79.51
3.778 2	212.98	40.15	451.43	54.34	772.96	79.44	1 206.30	81.77
4.000 0	220.12	32.19	461.47	45.27	788.71	71.01	1 223.20	76.19
4.397 9	228.12	20.11	472.92	28.78	813.25	61.67	1 244.90	54.54
4.699 0	231.59	11.52	477.57	15.44	820.02	22.48	1 254.30	31.22
5.000 0	234.90	11.00	480.53	9.83	825.05	16.71	1 260.00	18.94
5.397 9	236.51	4.05	483.73	8.04	829.22	10.48	1 265.20	13.07
6.000 0	240.75	7.04	489.33	9.30	841.05	19.65	1 274.90	16.11
7.000 0	243.70	2.95	495.82	6.49	861.34	20.29	1 295.30	20.40
8.000 0	244.12	0.42	497.01	1.19	865.96	4.62	1 302.30	7.00
9.000 0	244.17	0.05	497.14	0.13	866.51	0.55	1 303.10	0.80
10.000 0	244.18	0.01	497.15	0.01	866.58	0.07	1 303.20	0.10
11.000 0	244.18	0	497.16	0.01	866.59	0.01	1 303.20	0
12.000 0	244.18	0	497.16	0	866.59	0	1 303.20	0

Table 8. Comparison of natural frequency between V-shaped plate and elastic support isolated plate

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Table 8. Comparison of natural frequency between V-shaped plate and elastic support isolated plate

(m, n)阶模态	V形连接板固有频率f/Hz	弹性支撑矩形板固有频率f/Hz	相对变化/%
(1, 1)	128.84	133.45	3.45
(1, 2)	240.13	244.18	1.66
(2, 2)	338.86	349.21	2.96
(2, 3)	492.30	497.15	0.98
(3, 3)	633.21	649.39	2.49
(3, 4)	852.42	866.58	1.63
(4, 4)	1 033.10	1 066.80	3.26
(4, 5)	1 289.70	1 303.20	1.04

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Dong TANG, Maohui RAN, Ye LI, Hao WANG, Weipeng XIONG. Dynamic boundary characteristics for truncated model of V-shaped orthogonally stiffened plates[J]. Chinese Journal of Ship Research, 2025, 20(4): 173

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Paper Information

Category: Ship Structure and Fittings

Received: Mar. 26, 2024

Accepted: --

Published Online: Sep. 11, 2025

The Author Email:

DOI:10.19693/j.issn.1673-3185.03846

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Material properties and geometric parameters of the numerical model for V-shaped connecting plate

Table 1. Material properties and geometric parameters of the numerical model for V-shaped connecting plate

Table 2. Natural frequencies and their maximum differences of V-shaped connecting plates under different grid sizes

Table 2. Natural frequencies and their maximum differences of V-shaped connecting plates under different grid sizes

Table 3. Comparison between the results of this article and those of Reference [5]

Table 3. Comparison between the results of this article and those of Reference [5]

Table 4. The (m, n)-order natural frequencies f and their variation rate κ1 of V-shaped plates under different coupling angles α

Table 4. The (m, n)-order natural frequencies f and their variation rate κ1 of V-shaped plates under different coupling angles α

Table 5. The (m, n)-order natural frequencies f and their variation rate κ2 of V-shaped plates under different thickness of the attached plate

Table 5. The (m, n)-order natural frequencies f and their variation rate κ2 of V-shaped plates under different thickness of the attached plate

Table 6. The (m, n)-order natural frequencies f and their variation rate κ3 of V-shaped plates under different length of the attached plate

Table 6. The (m, n)-order natural frequencies f and their variation rate κ3 of V-shaped plates under different length of the attached plate

Table 7. The natural frequency f and their variation rate κ4 of isolated plate under different elastic support stiffness

Table 7. The natural frequency f and their variation rate κ4 of isolated plate under different elastic support stiffness

Table 8. Comparison of natural frequency between V-shaped plate and elastic support isolated plate

Table 8. Comparison of natural frequency between V-shaped plate and elastic support isolated plate

Table 4. The (m, n)-order natural frequencies f and their variation rate κ₁ of V-shaped plates under different coupling angles α

Table 4. The (m, n)-order natural frequencies f and their variation rate κ₁ of V-shaped plates under different coupling angles α

Table 5. The (m, n)-order natural frequencies f and their variation rate κ₂ of V-shaped plates under different thickness of the attached plate

Table 5. The (m, n)-order natural frequencies f and their variation rate κ₂ of V-shaped plates under different thickness of the attached plate

Table 6. The (m, n)-order natural frequencies f and their variation rate κ₃ of V-shaped plates under different length of the attached plate

Table 6. The (m, n)-order natural frequencies f and their variation rate κ₃ of V-shaped plates under different length of the attached plate

Table 7. The natural frequency f and their variation rate κ₄ of isolated plate under different elastic support stiffness

Table 7. The natural frequency f and their variation rate κ₄ of isolated plate under different elastic support stiffness