Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

Table 3

The first nondimensional fundamental frequencies with different meshes.

Cases of GPL		UD-type		X-type		O-type		V-type
BC		SSSS	CCCC	SSSS	CCCC	SSSS	CCCC	SSSS	CCCC
SPH (spherical shell)
Mesh	4 × 4	28.9466	45.7319	29.7675	44.5987	23.9914	39.9593	25.9421	41.9856
	6 × 6	28.9305	45.6370	29.7532	44.5122	23.9789	39.8547	25.9291	41.8878
	8 × 8	28.9279	45.6238	29.7508	44.4995	23.9769	39.8417	25.9270	41.8752
	10 × 10	28.9273	45.6202	29.7502	44.4959	23.9763	39.8384	25.9291	41.8719
	12 × 12	28.9270	45.6189	29.7500	44.4946	23.9761	39.8372	25.9264	41.8706
	14 × 14	28.9269	45.6183	29.7499	44.4940	23.9760	39.8367	25.9262	41.8701
[35]		29.5920	44.0300	30.8370	43.2450	25.3060	39.4860	27.4230	40.5730
CLY (cylindrical shell)
Mesh	4 × 4	27.0804	43.7319	28.4903	41.3521	22.7309	38.5900	24.5928	40.6802
	6 × 6	27.0659	43.6467	28.4761	41.2750	22.7179	38.4899	24.5792	40.5859
	8 × 8	27.0635	43.6348	28.4737	41.2635	22.7158	38.4780	24.5770	40.5741
	10 × 10	27.0629	43.6316	28.4731	41.2603	22.7152	38.4750	24.5764	40.5711
	12 × 12	27.0627	43.6304	28.4729	41.2590	22.7150	38.4739	24.5762	40.5700
	14 × 14	27.0626	43.6299	28.4728	41.2585	22.7149	38.4734	24.5761	40.5695
[35]		28.4430	42.4540	29.7630	41.7740	23.9830	37.9270	25.9830	39.0500