Free Vibration of Functionally Graded Sandwich Shallow Shells on Winkler and Pasternak Foundations with General Boundary Restraints

Table 4

Comparisons of nondimensional frequency parameters for Type and FGSSS with completely free boundary restraints, respectively (a=b, h/b=0.1, and R_xy=).

Mode	a/R=0.2						a/R=0.5
	12×12		13 ×13		14×14		12×12		13×13		14×14
	Jin et al. [44]	Pre-; sent	Jin et al. [44]	Pre-; sent	Jin et; al. [44]	Pre-; sent	Jin et al. [44]	Pre-; sent	Jin et al. [44]	Pre-; sent	Jin et al. [44]	Pre-; sent
Type : FG circular cylindrical shallow shell
1	0.903	0.907	0.902	0.905	0.902	0.905	0.901	0.903	0.901	0.902	0.901	0.902
2	1.352	1.361	1.352	1.359	1.352	1.358	1.405	1.411	1.405	1.411	1.405	1.410
3	1.662	1.670	1.662	1.666	1.662	1.659	1.734	1.738	1.734	1.735	1.734	1.735
4	2.279	2.285	2.278	2.281	2.278	2.281	2.272	2.275	2.271	2.276	2.271	2.276
Type : FG spherical shallow shell
1	0.902	0.905	0.902	0.905	0.902	0.902	0.899	0.904	0.898	0.901	0.898	0.897
2	1.335	1.336	1.335	1.336	1.335	2.334	1.322	1.325	1.322	1.325	1.322	1.325
3	1.696	1.691	1.696	1.694	1.696	1.695	1.900	1.905	1.900	1.905	1.900	1.905
4	2.279	2.284	2.279	2.284	2.279	2.284	2.274	2.276	2.274	2.275	2.274	2.275
Type : FG hyperbolic paraboloidal shallow shell
1	0.902	0.905	0.902	0.905	0.902	0.905	0.899	0.896	0.899	0.894	0.899	0.894
2	1.399	1.395	1.399	1.395	1.399	1.394	1.634	1.635	1.634	1.637	1.634	1.638
3	1.648	1.645	1.648	1.645	1.648	1.654	1.683	1.687	1.683	1.687	1.683	1.687
4	2.283	2.285	2.282	2.286	2.282	2.286	2.294	2.296	2.293	2.296	2.293	2.297
Type : FG circular cylindrical shallow shell
1	0.835	0.845	0.835	0.845	0.835	0.844	0.833	0.835	0.833	0.834	0.833	0.834
2	1.249	1.245	1.249	1.245	1.249	1.245	1.302	1.306	1.302	1.308	1.302	1.308
3	1.537	1.550	1.537	1.552	1.537	1.553	1.604	1.612	1.604	1.610	1.604	1.610
4	2.105	2.110	2.105	2.110	2.104	2.108	2.104	2.107	2.104	2.107	2.104	2.109
Type : FG spherical shallow shell
1	0.835	0.838	0.834	0.835	0.834	0.832	0.830	0.834	0.830	0.835	0.830	0.835
2	1.235	1.241	1.235	1.239	1.235	1.238	1.227	1.231	1.227	1.234	1.227	1.234
3	1.570	1.574	1.570	1.574	1.570	1.574	1.765	1.768	1.765	1.767	1.764	1.767
4	2.106	2.110	2.105	2.110	2.105	2.108	2.105	2.109	2.105	2.114	2.105	2.114
Type : FG hyperbolic paraboloidal shallow shell
1	0.836	0.841	0.835	0.838	0.835	0.837	0.832	0.835	0.832	0.836	0.832	0.836
2	1.291	1.294	1.291	1.294	1.291	1.294	1.507	1.521	1.507	1.521	1.507	1.520
3	1.522	1.532	1.522	1.537	1.522	1.540	1.555	1.547	1.555	1.549	1.555	1.551
4	2.101	2.104	2.101	2.114	2.104	2.107	2.106	2.115	2.105	2.114	2.105	2.114