## 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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