Free Vibration of Laminated Composite Hypar Shell Roofs with Cutouts

Table 5

Clamping options for +45/−45/+45/−45 hypar shells with central cutouts having a′/a ratio 0.2.

Number of sides to be clamped	clamped edges	Improvement of frequencies with respect to simply supported shells	Marks indicating the efficiencies of clamping
0	Simply supported no edges clamped (SSSS)	—	0
1	(a) Along 𝑥=0 (CSSS)	Slight improvement	9
	(b) along 𝑥=𝑎 (SSCS)	Slight improvement	9
	(c) along 𝑦=𝑏 (SSSC)	Slight improvement	10
2	(a) Two alternate edges (CSCS, SCSC)	Good improvement	22
	(b) Two adjacent edges (CSSC, CCSS)	Marked improvement	52
3	3 edges excluding 𝑦=0 CSCC	Remarkable improvement	72
	3 edges excluding 𝑥=𝑎 CCSC	Remarkable improvement	72
	3 edges excluding 𝑦=𝑏 CCCS	Remarkable improvement	72
4	All sides (CCCC)	Frequency attains a maximum value	100