Free Vibration of Laminated Composite Hypar Shell Roofs with Cutouts

Table 7

Values of “𝑟” for +45/−45/+45/−45 hypar shells.

Edge condition	𝑦	𝑥
		0.2	0.3	0.4	0.5	0.6	0.7	0.8
CCCC	0.2	97.79	94.67	95.97	102.56	95.97	94.82	97.78
	0.3	94.87	94.55	96.55	101.00	96.53	94.55	94.87
	0.4	95.96	96.43	97.07	98.73	97.07	96.43	95.95
	0.5	102.07	100.76	98.61	98.80	98.61	100.76	101.92
	0.6	95.95	96.43	97.10	98.77	97.07	96.43	95.95
	0.7	94.87	94.55	96.52	100.99	96.52	94.55	94.87
	0.8	97.79	94.82	95.97	102.30	95.97	94.82	97.78
CSCC	0.2	97.57	94.48	97.00	104.29	97.32	94.75	97.73
	0.3	99.55	97.12	98.28	101.72	98.39	97.16	99.54
	0.4	100.05	97.96	97.40	99.02	97.28	97.79	101.05
	0.5	100.24	97.51	94.53	93.90	94.31	97.28	100.18
	0.6	97.85	95.01	91.14	90.09	90.91	94.74	97.89
	0.7	97.55	92.19	87.69	86.65	87.45	91.90	97.32
	0.8	97.21	90.03	85.03	84.15	84.80	89.75	97.08
CCSC	0.2	97.20	97.40	98.19	100.24	99.74	99.45	97.77
	0.3	89.82	91.97	94.82	97.28	97.77	97.17	94.74
	0.4	84.74	87.48	90.99	94.48	97.44	98.49	97.24
	0.5	84.02	86.63	90.17	94.16	99.51	102.03	104.53
	0.6	84.74	87.47	90.99	94.48	97.44	98.49	97.24
	0.7	89.82	91.97	94.82	97.28	97.77	97.17	94.74
	0.8	97.20	97.40	98.19	100.24	99.74	99.48	97.77
CCCS	0.2	97.12	89.92	85.08	84.42	85.08	89.92	97.12
	0.3	97.36	92.03	87.73	86.93	87.73	92.03	97.36
	0.4	98.00	94.81	91.17	90.40	91.17	94.81	98.00
	0.5	100.15	97.25	90.40	94.22	94.51	97.25	100.15
	0.6	99.96	97.83	97.38	99.37	97.38	97.83	100.67
	0.7	99.58	97.23	98.44	101.84	98.44	97.23	99.95
	0.8	97.74	94.71	97.22	104.30	97.22	94.71	97.76
CSSC	0.2	98.26	99.11	101.00	99.30	96.94	95.60	95.03
	0.3	90.66	92.23	94.92	97.24	97.39	96.69	95.59
	0.4	86.66	88.94	92.14	95.13	96.60	97.47	96.95
	0.5	89.02	91.38	93.92	94.86	94.78	97.23	99.41
	0.6	95.40	97.29	97.18	93.64	91.91	94.83	100.96
	0.7	98.69	98.73	96.98	91.14	88.82	92.16	99.05
	0.8	99.02	98.80	95.27	88.93	86.67	90.63	98.26
CCSS	0.2	99.03	98.82	95.03	88.84	86.67	90.65	98.33
	0.3	98.70	98.68	96.83	91.07	88.82	92.17	99.06
	0.4	95.40	97.30	97.09	93.59	91.92	94.84	100.99
	0.5	89.01	91.37	93.87	94.82	94.96	97.25	99.42
	0.6	86.65	88.93	92.10	95.10	96.61	97.47	96.93
	0.7	90.63	92.21	94.89	97.22	97.39	96.69	95.57
	0.8	98.26	99.07	100.96	99.30	96.95	95.63	95.03
CSCS	0.2	98.68	99.70	96.60	94.59	96.60	99.70	98.68
	0.3	100.35	100.95	99.60	98.53	99.60	100.95	100.35
	0.4	100.63	101.43	100.62	99.97	100.62	101.43	100.62
	0.5	100.75	101.79	101.07	100.45	101.07	101.79	100.75
	0.6	100.63	101.43	100.62	99.97	100.62	101.43	100.62
	0.7	100.35	100.95	99.60	98.53	99.60	100.95	100.35
	0.8	98.68	99.70	96.60	94.59	96.60	99.70	98.68
SCSC	0.2	98.88	100.37	100.64	100.83	100.64	100.37	98.88
	0.3	99.76	101.04	101.52	101.86	101.53	101.04	99.75
	0.4	96.65	99.74	100.713	101.14	100.76	99.74	96.64
	0.5	94.69	98.67	100.09	100.53	100.09	98.67	94.69
	0.6	96.64	99.74	100.76	101.14	100.76	99.74	96.64
	0.7	99.76	101.04	101.53	101.86	101.52	101.04	99.75
	0.8	98.88	100.37	100.64	100.83	100.64	100.37	98.88
CSSS	0.2	97.88	98.69	96.54	93.98	94.57	97.61	98.39
	0.3	99.43	99.86	99.39	98.38	98.64	99.79	99.86
	0.4	99.76	100.55	100.55	100.23	100.53	101.37	101.32
	0.5	100.33	101.13	100.94	100.64	101.07	102.09	101.97
	0.6	99.76	100.55	100.55	100.23	100.52	101.54	101.32
	0.7	99.43	99.86	99.39	98.38	98.64	99.80	99.86
	0.8	97.88	98.68	96.54	93.98	94.57	97.61	98.39
SSSC	0.2	98.24	99.78	101.36	102.07	101.36	99.77	98.24
	0.3	97.52	99.76	101.40	102.14	101.40	99.76	97.51
	0.4	94.58	98.68	100.53	101.03	100.53	98.68	94.58
	0.5	94.08	98.44	100.24	100.63	100.24	98.44	94.08
	0.6	96.58	99.47	100.62	100.96	100.62	99.47	96.57
	0.7	98.72	99.90	100.61	101.15	100.61	99.90	98.72
	0.8	98.03	99.41	99.73	100.34	99.72	99.41	98.03
SSCS	0.2	98.39	97.61	94.57	93.99	96.55	98.69	97.88
	0.3	99.87	99.80	98.65	98.39	99.40	99.87	99.43
	0.4	101.32	101.38	100.53	100.23	100.55	100.56	99.76
	0.5	101.98	102.10	101.07	100.64	100.95	101.13	100.33
	0.6	101.33	101.38	100.53	100.23	100.55	100.56	99.76
	0.7	99.87	99.80	98.65	98.39	99.40	99.87	99.43
	0.8	98.39	97.62	94.58	93.99	96.54	98.69	97.88
SSSS	0.2	97.32	97.03	111.45	93.16	94.72	97.03	97.32
	0.3	96.96	98.53	98.61	98.09	98.62	98.53	96.96
	0.4	94.66	98.58	100.57	100.43	100.57	98.58	94.65
	0.5	93.19	98.05	100.34	100.80	100.34	98.05	93.18
	0.6	94.65	98.58	100.57	100.43	100.57	98.58	94.65
	0.7	96.95	98.53	98.61	98.09	98.62	98.53	96.96
	0.8	97.31	97.03	94.72	93.16	94.72	97.03	97.32

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.