Haar Wavelet Method for Nonlinear Vibration of Functionally Graded CNT-Reinforced Composite Beams Resting on Nonlinear Elastic Foundations in Thermal Environment

Table 3

Comparison of the first three dimensionless linear frequency parameters for CNTRC beams resting on linear elastic foundations ( = 0.12,  = 15, , and  = 0; boundary condition: H-H).

Type		( = 0,  = 0)			( = 0.1,  = 0)			( = 0.1,  = 0.02)
		UD	Present	0.9739	2.8641	4.8515	1.0229	2.8811	4.8616	1.1132	3.0120	5.0371
Ref. [23]	0.9753		2.8728	4.8704	1.0241	2.8898	4.8804	1.1144	3.0203	5.0552
FG-X	Present	1.1129	3.0702	5.0473	1.1560	3.0860	5.0570	1.2367	3.2087	5.2261
	Ref. [23]	1.1150	3.0814	5.0695	1.1581	3.0972	5.0791	1.2386	3.2194	5.2474
FG-O	Present	0.7521	2.4507	4.4175	0.8145	2.4705	4.4285	0.9253	2.6216	4.6200
	Ref. [23]	0.7527	2.4562	4.4320	0.8150	2.4760	4.4430	0.9258	2.6268	4.6338