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

Table 2

Convergence of linear fundamental frequency parameters for C-C FG-CNTRC beams (,  = 25, and ; the number in parenthesis indicates the estimated rate of convergence).

	Type	Present					Ref. [18]
		0.12	FG-X	1.175828	1.173992	1.173533 (2.000)		1.173417 (1.984)	1.173389 (2.051)	1.1733
UD	1.073922		1.071476	1.070863 (1.996)	1.070709 (1.993)	1.070671 (2.019)	1.0706
FG-O	0.887362		0.883423	0.882435 (1.995)	0.882188 (2.000)	0.882126 (1.994)	0.8821
0.28	FG-X	1.691824	1.689592	1.689034 (2.000)	1.688894 (1.995)	1.688859 (2.000)	1.6887
	UD	1.536038	1.533217	1.532510 (1.996)	1.532333 (1.998)	1.532289 (2.008)	1.5322
	FG-O	1.297611	1.292688	1.291453 (1.995)	1.291144 (1.999)	1.291067 (2.005)	1.2911