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

Following the Rayleigh-Ritz procedure, we substitute for $$w$$ using equation 5 in equation 4, carry out the double integrations, and differentiate with respect to each of the $$c_i$$ in turn. Setting the derivatives equal to zero then results in a set of algebraic equations for the $$c_i$$:
 $$\mathbf{A} \mathbf{c} = \mathbf{B} \mathbf{g}$$
(Eqn. 8)
where the components of $$\mathbf{g}$$ represent the nodal values of the pressure field $$g$$.

The components of the matrices $$\mathbf{A}$$ and $$\mathbf{B}$$ are functions of $$\lambda$$ (which depends on the frequency, tension and area density) and of the vertex coördinates of the triangular element.

R. Funnell