Table 2 Comparison between the numerical frequency \(\omega\), the approximate frequency obtained by present method (given in Eq. 13) and other existing frequency (Hamdan and Dado 1997; Wu et al. 2003) for \(\alpha = \beta = 2\) as well as several large amplitudes
A | Numerical frequency \(\omega_{e}\) | Hamdan and Dado (1997) (error%) | Wu et al. (2003) (error%) | Present method (error%) \(\omega_{0}\) | ||
|---|---|---|---|---|---|---|
\(\omega_{0}\) | \(\omega_{1}\) | \(\omega_{0}\) | \(\omega_{1}\) | |||
5 | 1.37132 | 1.21687 | 1.25786 | 1.21687 | 1.34073 | 1.39406 |
11.26 | 8.27 | 11.26 | 2.23 | 1.66 | ||
10 | 1.40006 | 1.22272 | 1.26541 | 1.22272 | 1.35613 | 1.40898 |
12.67 | 9.61 | 12.67 | 3.14 | 0.64 | ||
15 | 1.40707 | 1.22384 | 1.26685 | 1.22384 | 1.35913 | 1.41187 |
13.02 | 9.96 | 13.02 | 3.41 | 0.34 | ||
20 | 1.40986 | 1.22424 | 1.26736 | 1.22424 | 1.36020 | 1.41289 |
13.17 | 10.11 | 13.17 | 3.52 | 0.22 | ||
25 | 1.41127 | 1.22442 | 1.26760 | 1.22442 | 1.36069 | 1.41337 |
13.24 | 10.18 | 13.24 | 3.59 | 0.15 | ||
30 | 1.41207 | 1.22452 | 1.26773 | 1.22452 | 1.36096 | 1.41363 |
13.28 | 10.22 | 13.28 | 3.62 | 0.11 | ||
50 | 1.41335 | 1.22466 | 1.26791 | 1.22466 | 1.36135 | 1.41400 |
13.35 | 10.29 | 13.35 | 3.68 | 0.05 | ||
100 | 1.41397 | 1.22472 | 1.26799 | 1.22472 | 1.36152 | 1.41416 |
13.39 | 10.32 | 13.39 | 3.71 | 0.01 | ||
200 | 1.41414 | 1.22474 | 1.26801 | 1.22474 | 1.36156 | 1.41420 |
13.40 | 10.33 | 13.40 | 3.72 | 0.00 | ||
500 | 1.41420 | 1.22474 | 1.26802 | 1.22474 | 1.36157 | 1.41421 |
13.40 | 10.33 | 13.40 | 3.72 | 0.00 | ||
1000 | 1.41421 | 1.22474 | 1.26802 | 1.22474 | 1.36158 | 1.41421 |
13.40 | 10.34 | 13.40 | 3.72 | 0.00 | ||