Eigenfrequencies or ‘Eigenvalues’ are non-zero solutions to the behaviour of a dynamic system under certain boundary conditions. In this case, a thin rectangular stainless steel plate which is pinned at its four corners (being held down) of dimensions of an A4 sheet of paper is being simulated. Displacement of the plate is shown according to intensity of the colour, where red indicates the plate is bending out of the screen, and blue indicating plate is bending into the screen. White indicates zero displacement, the plate is not bending.
These are simulations of the static magnetic field of a cylindrical coil, such as one you get in a loudspeaker.
The second photograph shows a simulation of a flat-coil, or ‘pancake coil’ as It is setup.