 Flexural wave

For a thin plate with areal mass $m$ and bending stiffness $B$, small free transverse disturbances satisfy $m{\eta }_{tt}+B{\nabla }^4\eta =0$. A plane wave of tangential wavenumber $k$ therefore satisfiesThe frequency is quadratic in wavenumber, so these waves are dispersive. Matching this free-wave relation cancels the plate's inertial and bending response in an acoustic transmission problem.