## 3. A simple element analysis (cont'd)

The differential equation governing a plane membrane under tension and
vibrating sinusoidally (Rayleigh, 1877) is

$T{\nabla}^{2}w+\sigma {\omega}^{2}w=p$
| (Eqn. 3) |

where
- \(w\) is the membrane displacement (m);
- \(\sigma\) is the area density (kg m
^{−2});
- \(\omega\) is the angular frequency (s
^{−1});
- \(T\) is the tension (N m
^{−1}); and
- \(p\) is applied pressure (N m
^{−2}).

R. Funnell
Last modified: 2018-11-07 12:52:06
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