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 2

Convergence of frequency parameters of the single curved shells with different coupling parameters .

Shape	Mode
		10^1	10^3	10^5	10^7	10^8	10^10	10^12	10^14	10^16	10^18
Cylindrical shells	1	10.043	10.043	10.058	10.680	11.659	16.469	16.779	16.780	16.780	16.780
	2	10.051	10.051	10.062	11.315	14.581	16.681	16.779	16.780	16.780	16.780
	3	16.515	16.515	16.518	16.685	16.857	17.399	17.711	17.714	17.714	17.714
	4	17.203	17.203	17.204	17.215	17.236	17.399	17.711	17.714	17.714	17.714
	5	17.564	17.564	17.566	17.744	19.153	21.296	21.381	21.381	21.381	21.381
	6	19.644	19.644	19.645	19.685	19.762	21.374	21.381	21.381	21.381	21.381
Conical shells	1	10.376	10.376	10.391	11.164	12.259	17.946	18.161	18.162	18.162	18.162
	2	10.392	10.392	10.418	12.431	16.393	17.985	18.161	18.162	18.162	18.162
	3	17.786	17.786	17.790	17.990	18.164	18.915	19.280	19.286	19.286	19.286
	4	18.553	18.553	18.557	18.676	18.693	18.994	19.280	19.286	19.286	19.286
	5	18.725	18.725	18.726	19.009	20.736	21.794	21.855	21.855	21.855	21.855
	6	20.595	20.595	20.602	21.018	21.415	21.802	21.855	21.855	21.855	21.855
Spherical shells	1	9.766	9.761	9.757	9.867	10.088	11.761	12.034	12.038	12.038	12.038
	2	9.766	9.764	9.769	10.017	10.809	11.827	12.036	12.038	12.038	12.038
	3	12.046	12.046	12.046	12.055	12.086	12.163	12.221	12.224	12.224	12.224
	4	12.117	12.117	12.118	12.133	12.153	12.185	12.223	12.224	12.224	12.224
	5	12.308	12.308	12.319	12.321	12.340	12.672	13.084	13.089	13.089	13.089
	6	12.493	12.493	12.493	12.523	12.665	12.947	13.085	13.089	13.089	13.089