Free Vibration of Laminated Composite Hypar Shell Roofs with Cutouts

Table 6

Values of “𝑟” for 0/90/0/90 hypar shells.

Edge condition	𝑦	𝑥
		0.2	0.3	0.4	0.5	0.6	0.7	0.8
CCCC	0.2	98.34	98.04	97.82	97.7	97.77	97.98	98.29
	0.3	98.13	97.49	96.74	96.4	96.71	97.46	98.1
	0.4	98.02	96.88	95.55	95.04	95.54	96.88	98.02
	0.5	97.98	96.62	95.08	94.52	95.08	96.62	97.98
	0.6	98.02	96.88	95.54	95.04	95.55	96.88	98.02
	0.7	98.1	97.46	96.71	96.4	96.74	97.49	98.13
	0.8	98.29	97.98	97.77	97.71	97.82	98.04	98.34
CSCC	0.2	96.11	96.68	96.37	96.31	96.38	96.67	97.25
	0.3	96.11	95.46	95.31	95.45	95.38	95.50	96.1
	0.4	95.35	94.72	94.81	95.51	94.88	94.75	95.36
	0.5	95.27	94.51	94.49	96.13	94.49	94.52	95.27
	0.6	95.49	94.58	94.05	93.43	94.03	94.59	95.51
	0.7	95.83	94.81	93.71	92.57	93.68	94.83	95.87
	0.8	102.93	95.19	93.75	92.41	93.74	95.22	96.33
CCSC	0.2	96.19	95.74	95.42	95.26	95.36	95.95	97.05
	0.3	95.08	94.73	94.51	94.50	94.77	95.49	96.76
	0.4	93.26	93.26	93.65	94.21	94.77	95.44	96.73
	0.5	91.67	91.87	92.74	94.12	95.51	95.61	96.81
	0.6	93.21	93.21	93.58	94.15	94.77	95.48	96.76
	0.7	95.05	94.69	94.47	94.48	94.80	95.57	96.84
	0.8	96.19	95.73	95.41	95.28	95.42	96.08	97.17
CCCS	0.2	96.32	95.22	93.73	92.33	93.65	95.16	95.16
	0.3	95.86	94.83	93.65	92.44	93.59	94.78	95.83
	0.4	95.50	94.59	94.02	93.38	93.97	94.56	95.48
	0.5	95.28	94.52	94.47	95.68	94.43	94.49	95.26
	0.6	95.34	94.49	94.85	95.51	94.79	94.71	95.33
	0.7	96.08	95.50	95.37	95.45	95.31	95.46	96.09
	0.8	97.23	96.67	96.38	96.31	96.37	96.68	97.28
CSSC	0.2	96.08	95.31	94.74	94.43	94.54	95.05	95.64
	0.3	95.38	95.13	95.25	95.43	95.50	95.44	95.10
	0.4	91.75	91.74	92.23	93.10	94.94	95.44	94.57
	0.5	90.85	90.57	90.76	91.46	93.56	95.23	94.56
	0.6	92.37	91.62	91.32	91.40	92.88	94.92	94.98
	0.7	94.10	93.04	92.27	91.43	92.24	94.84	95.64
	0.8	95.61	94.49	93.33	91.74	92.13	95.18	96.46
CCSS	0.2	95.54	94.41	93.26	91.63	91.98	94.95	96.31
	0.3	94.05	92.98	92.21	91.34	92.10	94.66	95.50
	0.4	92.36	91.61	91.32	91.34	92.80	94.77	94.87
	0.5	90.91	90.66	90.80	91.76	93.68	95.11	94.50
	0.6	91.71	91.75	92.27	93.17	95.24	95.40	94.55
	0.7	95.28	95.03	95.14	95.36	95.47	95.43	95.11
	0.8	95.96	95.22	94.69	94.44	94.62	95.18	95.77
CSCS	0.2	99.07	100.14	98.96	98.08	98.93	100.14	99.10
	0.3	99.27	100.79	99.18	97.98	99.14	100.76	99.28
	0.4	99.56	101.15	99.46	98.20	99.44	101.13	99.55
	0.5	99.67	101.24	99.57	98.33	99.56	101.24	99.67
	0.6	99.54	101.13	99.44	98.20	99.45	101.15	99.55
	0.7	99.28	100.76	99.14	97.98	99.17	100.78	99.27
	0.8	99.10	100.14	98.92	98.08	98.95	100.14	99.07
SCSC	0.2	99.04	99.30	99.56	99.67	99.56	99.27	98.99
	0.3	100.18	100.79	101.13	101.23	101.14	100.81	100.18
	0.4	99.04	99.22	99.43	99.54	99.44	99.23	99.04
	0.5	98.17	98.07	98.20	98.29	98.20	98.07	98.17
	0.6	99.04	99.23	99.44	99.54	99.43	99.22	99.04
	0.7	100.18	100.82	101.14	101.23	101.13	100.80	100.18
	0.8	98.99	99.27	99.56	99.82	99.56	99.30	99.04
CSSS	0.2	98.49	98.97	98.19	97.42	97.62	98.61	98.94
	0.3	98.82	99.92	99.27	98.39	98.59	99.53	99.48
	0.4	99.28	100.60	99.91	98.83	98.95	99.95	99.89
	0.5	99.44	100.78	100.07	98.95	99.07	100.12	100.07
	0.6	99.26	100.59	99.89	98.82	98.97	99.98	99.89
	0.7	98.83	99.91	99.22	98.37	98.62	99.58	99.49
	0.8	98.54	99.02	98.17	97.43	97.67	98.65	98.93
SSSC	0.2	98.92	99.40	99.86	100.08	99.87	99.41	98.90
	0.3	98.71	99.58	99.94	100.10	99.95	99.59	98.70
	0.4	97.69	98.68	98.96	99.05	98.96	98.67	97.67
	0.5	97.44	98.46	98.82	98.91	98.82	98.44	97.42
	0.6	98.23	99.29	99.86	100.01	99.85	99.27	98.22
	0.7	99.00	99.94	100.56	100.74	100.55	99.93	99.01
	0.8	98.39	98.81	99.26	99.43	99.26	98.83	98.45
SSCS	0.2	98.93	98.65	97.68	97.42	98.18	99.02	98.55
	0.3	99.48	99.58	98.62	98.37	99.22	99.91	98.83
	0.4	99.89	99.98	98.96	98.82	99.88	100.59	99.27
	0.5	100.08	100.12	99.06	98.94	100.06	100.78	99.45
	0.6	99.88	99.95	98.94	98.82	99.90	100.60	99.27
	0.7	99.48	99.53	98.58	98.39	99.26	99.91	98.81
	0.8	98.94	98.60	97.61	97.42	98.17	98.96	98.49
SSSS	0.2	97.78	97.55	96.93	96.64	96.85	97.51	97.94
	0.3	98.22	99.14	98.94	98.81	98.80	98.99	98.06
	0.4	97.52	99.41	99.42	99.28	99.24	99.20	97.43
	0.5	97.22	99.41	99.58	99.37	99.59	99.41	97.22
	0.6	97.44	99.20	99.23	99.27	99.43	99.41	97.52
	0.7	98.06	98.99	98.80	98.81	98.93	99.14	98.22
	0.8	97.94	97.50	96.84	96.66	96.93	97.55	97.78

𝑎/𝑏=1, 𝑎/ℎ=100, 𝑎′0𝑥02044𝑏′=1, 𝑐/𝑎=0.2; 𝐸₁₁/𝐸₂₂ = 25, 𝐺₂₃ = 0.2𝐸₂₂, 𝐺₁₃ = 𝐺₁₂ = 0.5𝐸₂₂, 𝜈₁₂=𝜈₂₁=0.25.