Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Table 2

Convergence of frequency parameter for Al/Al₂O₃ shallow shells with SSSS boundary constraints (, , , ).

Type		Mode number
		1	2	3	4	5	6	7	8
Plate		4.417	10.585	10.585	16.195	16.195	16.303	19.910	19.910
		4.417	10.585	10.585	16.195	16.195	16.303	19.908	19.908
		4.417	10.585	10.585	16.195	16.195	16.303	19.907	19.907
		4.417	10.585	10.585	16.195	16.195	16.303	19.906	19.906
		4.417	10.585	10.585	16.195	16.195	16.303	19.906	19.906
		4.417	10.585	10.585	16.195	16.195	16.303	19.906	19.906
Cylindrical shell		5.739	10.493	12.308	16.053	16.195	16.613	19.880	21.162
		5.739	10.493	12.308	16.053	16.195	16.613	19.877	21.159
		5.739	10.493	12.308	16.053	16.195	16.613	19.877	21.159
		5.739	10.493	12.308	16.053	16.195	16.613	19.876	21.158
		5.739	10.493	12.308	16.053	16.195	16.613	19.876	21.158
		5.739	10.493	12.308	16.053	16.195	16.613	19.876	21.158
Spherical shell		8.946	13.139	13.139	16.053	16.053	18.082	21.422	21.422
		8.946	13.139	13.139	16.053	16.053	18.082	21.419	21.419
		8.946	13.139	13.139	16.053	16.053	18.082	21.419	21.419
		8.946	13.139	13.139	16.053	16.053	18.082	21.418	21.418
		8.946	13.139	13.139	16.053	16.053	18.082	21.418	21.418
		8.946	13.139	13.139	16.053	16.053	18.082	21.418	21.418
Hyperbolic paraboloidal shell		3.609	10.940	11.121	15.434	16.053	16.334	20.271	20.706
		3.609	10.940	11.121	15.434	16.053	16.334	20.269	20.703
		3.609	10.940	11.121	15.434	16.053	16.334	20.268	20.703
		3.609	10.940	11.121	15.434	16.053	16.334	20.268	20.702
		3.609	10.940	11.121	15.434	16.053	16.334	20.268	20.702
		3.609	10.940	11.121	15.434	16.053	16.334	20.268	20.702