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

Table 4

Nonlinear central deflection response of a simply supported beam: solutions with varying number of terms in time domain series $N_s$.

Time (s)	$N_s=1$	$N_s=3$	$N_s=5$	Woinowsky-Krieger [1]	Error 1	Error 2	Error 3
0.0050	0.8622	0.8566	0.8553	0.8533	1.0505	0.3895	0.2405
0.0100	0.4811	0.4720	0.4700	0.4665	3.1360	1.1828	0.7540
0.0150	$-$0.0420	$-$0.0398	$-$0.0395	$-$0.0404	3.7991	$-$1.6178	$-$2.2036
0.0300	$-$0.9965	$-$0.9939	$-$0.9942	$-$0.9963	0.0134	$-$0.2437	$-$0.2146
0.0400	$-$0.4060	$-$0.3952	$-$0.3938	$-$0.3928	3.3588	0.6230	0.2717
0.0450	0.1259	0.1240	0.1231	0.1210	4.0692	2.4780	1.7217
0.0550	0.9335	0.9300	0.9297	0.9286	0.5294	0.1543	0.1177
0.0650	0.7672	0.7596	0.7574	0.7545	1.6804	0.6677	0.3804
0.0750	$-$0.2086	$-$0.2022	$-$0.2010	$-$0.2009	3.8259	0.6691	0.0613
0.0850	$-$0.9596	$-$0.9547	$-$0.9549	$-$0.9566	0.3065	$-$0.2001	$-$0.1767
0.0900	$-$0.9698	$-$0.9655	$-$0.9657	$-$0.9676	0.2261	$-$0.2173	$-$0.1960
0.0950	$-$0.7113	$-$0.6999	$-$0.6983	$-$0.6974	1.9872	0.3496	0.1245
0.1000	$-$0.2477	$-$0.2404	$-$0.2390	$-$0.2387	3.7615	0.7006	0.1317