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