The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Table 1

The corresponding spring stiffness values for general boundary conditions.

Edges	BC	Essential conditions	Corresponding spring stiffness values
				F		0	0	0	0	0
C		10^8		10^8	10^8	10^8	10^8
S		10^8		10^8	10^8	0	10^8
E^1	;	10^2		10^2	10^8	10^8	10^8
E^2	;	10^8		10^8	10^2	10^8	10^8
E^3	, ;	10^8		10^8	10^8	10^2	10^2
	F		0	0	0	0	0
	C		10^8	10^8	10^8	10^8	10^8
	S		10^8	10^8	10^8	10^8	0
	E^1	;	10^2	10^2	10^8	10^8	10^8
	E^2	;	10^8	10^8	10^2	10^8	10^8
	E^3	, ;	10^8	10^8	10^8	10^2	10^2