An analytical coupled technique for solving nonlinear large-amplitude oscillation of a conservative system with inertia and static non-linearity

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Table 1 Comparison between the numerical frequency \(\omega\), the approximate frequency obtained by present method (given in Eq. 13) and other existing frequencies (Hamdan and Dado 1997; Wu et al. 2003) for \(\alpha = \beta = 1\) as well as several large amplitudes

A	Numerical frequency \(\omega_{e}\)	Hamdan and Dado (1997) (error%)		Wu et al. (2003) (error%)		Present method (error%) \(\omega_{0}\)
A	Numerical frequency \(\omega_{e}\)	\(\omega_{0}\)	\(\omega_{1}\)	\(\omega_{0}\)	\(\omega_{1}\)	Present method (error%) \(\omega_{0}\)
5	1.34288	1.20953	1.24841	1.20953	1.32217	1.37581
5	1.34288	9.93	7.04	9.93	1.54	2.45
10	1.38928	1.22074	1.26285	1.22074	1.35084	1.40388
10	1.38928	12.13	9.10	12.13	2.77	1.05
15	1.40138	1.22295	1.26570	1.22295	1.35672	1.40955
15	1.40138	12.73	9.68	12.73	3.19	0.58
20	1.40632	1.22373	1.26671	1.22373	1.35883	1.41158
20	1.40632	12.98	9.92	12.98	3.38	0.38
25	1.40883	1.22409	1.26718	1.22409	1.35981	1.41252
25	1.40883	13.11	10.05	13.11	3.48	0.26
30	1.41029	1.22429	1.26743	1.22429	1.36035	1.41304
30	1.41029	13.19	10.13	13.19	3.54	0.20
50	1.41261	1.22458	1.26781	1.22458	1.36113	1.41379
50	1.41261	13.31	10.25	13.31	3.65	0.08
100	1.41375	1.22470	1.26797	1.22470	1.36147	1.41411
100	1.41375	13.37	10.31	13.37	3.70	0.03
200	1.41408	1.22473	1.26801	1.22473	1.36155	1.41419
200	1.41408	13.39	10.33	13.39	3.72	0.00
500	1.41419	1.22474	1.26802	1.22474	1.36157	1.41421
500	1.41419	13.40	10.33	13.40	3.72	0.00
1000	1.41421	1.22474	1.26802	1.22474	1.36157	1.41421
1000	1.41421	13.40	10.33	13.40	3.72	0.00