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).

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