A Semianalytical Method for Nonlinear Vibration of Euler-Bernoulli Beams with General Boundary Conditions

Table 5

Nonlinear central deflection response of a simply supported beam: solutions with varying total number of sampling points $N$.

Time (s)	$N=9$	$N=11$	$N=13$	Woinowsky-Krieger [1]	Error 4	Error 5	Error 6
0.0050	0.8566	0.8562	0.8562	0.8533	0.3895	0.3458	0.3484
0.0100	0.4720	0.4711	0.4712	0.4665	1.1828	0.9922	1.0026
0.0150	$-$0.0398	$-$0.0410	$-$0.0410	$-$0.0404	$-$1.6178	1.4624	1.4228
0.0300	$-$0.9939	$-$0.9967	$-$0.9967	$-$0.9963	$-$0.2437	0.0411	0.0378
0.0400	$-$0.3952	$-$0.3969	$-$0.3970	$-$0.3928	0.6230	1.0606	1.0657
0.0450	0.1240	0.1223	0.1223	0.1210	2.4780	1.0651	1.0839
0.0500	0.6106	0.6097	0.6097	0.6048	0.9513	0.7984	0.8054
0.0650	0.7596	0.7585	0.7586	0.7545	0.6677	0.5300	0.5335
0.0750	$-$0.2022	$-$0.2033	$-$0.2033	$-$0.2009	0.6691	1.1924	1.1903
0.0850	$-$0.9547	$-$0.9580	$-$0.9579	$-$0.9566	$-$0.2001	0.1391	0.1377
0.0900	$-$0.9655	$-$0.9687	$-$0.9687	$-$0.9676	$-$0.2173	0.1140	0.1122
0.0950	$-$0.6999	$-$0.7017	$-$0.7017	$-$0.6974	0.3496	0.6071	0.6093
0.1000	$-$0.2404	$-$0.2415	$-$0.2415	$-$0.2387	0.7006	1.1716	1.1717