View source for Template:Free surface floating elastic plate relations

== Inner product between free surface and elastic plate modes ==

<center>
<math>
\int\nolimits_{-h}^{0}\phi_{n}(z)\psi_{m}(z) d z=B_{mn}
</math>
</center>
where
<center><math>
B_{mn}=\frac{k_{n}\sin k_{n}h\cos\kappa_{m}h-\kappa_{m}\cos k_{n}h\sin
\kappa_{m}h}{\left(  \cos k_{n}h\right) \left(  \cos \kappa_{m}h\right)  \left(  k_{n}
^{2}-\kappa_{m}^{2}\right)  }
</math></center>