Table 1 Computed results of Eq. (15)
Plate aspect ratio \( \frac{a}{b} \) | Numerator \( {\displaystyle \sum_{m=1}^{\infty }{\displaystyle \sum_{n=1}^{\infty}\frac{{\left(-1\right)}^{\frac{m+n}{2}\kern0.5em -1}}{mn\left(\frac{b}{a}{m}^2+\frac{a}{b}{n}^2\right)}}} \) | Denominator \( {\displaystyle \sum_{m=1}^{\infty }{\displaystyle \sum_{n=1}^{\infty}\frac{{\left(-1\right)}^{\frac{m+n}{2}\kern0.5em -1}}{mn{\left(\frac{b}{a}{m}^2+\frac{a}{b}{n}^2\right)}^2}}} \) | Ratio \( f\left(a,b,\frac{a}{2},\frac{b}{2}\right) \) |
|---|---|---|---|
1.0 | 0.44895 | 0.24409 | 1.839281 |
1.2 | 0.44059 | 0.23578 | 1.868649 |
1.5 | 0.40575 | 0.20627 | 1.967082 |
2.0 | 0.34749 | 0.15215 | 2.283865 |
3.0 | 0.24622 | 0.08167 | 3.014816 |
5.0 | 0.15405 | 0.031175 | 4.941460 |
7.5 | 0.10389 | 0.013907 | 7.470339 |
10.0 | 0.07859 | 0.007824 | 10.04473 |