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

Table 4

Comparison of the first three modes’ nondimension frequency and the nondimensional Winkler soil stiffness for a C-C beam.

C-C beam (linear)
λ	Present study	Present study	Present study	Ref. [11]	Exact; Ref. [12]	Error %	Error %	Error %
0	5,2153	4,8251	4,7775	4,7300	4,7300	−10,261	−2,011	−1,003
	8,5727	8,0083	7,9313	7,8500	7,8540	−9,150	−1,965	−0,984
	11,7658	11,2052	11,1030	11,0000	10,9960	−7,001	−1,902	−0,973
100	5,3833	5,0338	4,9919	4,9500	4,9500	−8,753	−1,692	−0,846
	8,6121	8,0565	7,9809	7,9000	7,9040	−8,959	−1,930	−0,973
	11,7811	11,2229	11,1212	11,0100	11,0140	−6,965	−1,897	−0,974
10000	10,1800	10,1328	10,1278	10,1200	10,1230	−0,563	−0,097	−0,047
	11,1400	10,8995	10,8692	10,8400	10,8390	−2,777	−0,558	−0,279
	13,0681	12,6693	12,5991	12,5300	12,5260	−4,328	−1,144	−0,583
1000000	31,6286	31,6271	31,6269	31,6400	31,6260	−0,008	−0,003	−0,003
	31,6654	31,6552	31,6540	31,6700	31,6530	−0,039	−0,007	−0,003
	31,7732	31,7467	31,7422	31,7500	31,7380	−0,111	−0,027	−0,013