A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations

Table 1

Comparison of the nondimensional frequencies corresponding to the first 3 modes and the nondimensional Winkler soil stiffness for a S-S beam.

S-S beam (linear)
λ	Present study	Present study	Present study	Ref. [10]	Ref. [11]	Exact; Ref. [12]	Average	Error %	Error %	Error %
0	3,131	3,141	3,141	3,150	3,141	3,141	3,144	0,427	0,104	0,092
	6,198	6,279	6,2822	6,280			6,280	1,304	0,013	−0,035
	9,139	9,411	9,421	9,420			9,420	2,982	0,092	−0,014
100	3,742	3,748	3,7483	3,750	3,748	3,7484	3,749	0,181	0,022	0,016
	6,300	6,378	6,3807	6,380			6,380	1,245	0,034	−0,010
	9,172	9,441	9,4511	9,450			9,450	2,945	0,093	−0,012
10000	10,024	10,024	10,024	10,020	10,024	10,024	10,023	−0,013	−0,016	−0,016
	10,350	10,368	10,368	10,360			10,360	0,095	−0,076	−0,082
	11,415	11,558	11,563	11,570			11,570	1,343	0,104	0,057
1000000	31,623	31,623	31,623	31,620	31,623	31,623	31,622	−0,004	−0,004	−0,004
	31,634	31,635	31,635	31,630			31,630	−0,016	−0,014	−0,014
	31,678	31,685	31,685	31,720			31,720	0,133	0,112	0,111