Behaviour and Optimization Aids of Composite Stiffened Hypar Shell Roofs with Cutout under Free Vibration

Table 5

Clamping options for 0/90/0/90 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)	Good improvement	21
	(b) Along 𝑥=𝑎 (SSCS)	Good improvement	21
	(c) Along 𝑦=𝑏 (SSSC)	Good improvement	21
2	(a) Two alternate edges (CSCS, SCSC)	Very good improvement	51
	(b) Two adjacent edges (CSSC, CCSS)	Marked improvement	71
3	3 edges excluding 𝑦=0 CSCC	Remarkable improvement and frequency becomes almost equal to that of fully clamped shells	85
	3 edges excluding 𝑥=𝑎 CCSC		85
	3 edges excluding 𝑦=𝑏 CCCS		85
4	All sides (CCCC)	Frequency attains a maximum value	100