I used to work in this world - I think Duncan's post #3 is good.
Circular geometries are a bit of a PITA to analyse, regarding modal behaviour - you end up dealing with the roots of Bessel functions. In general terms the modeshapes (or eigenvectors, if you're fancy) work in two ways, producing nodal lines which are either radial from the centre to the rim, or concentric - or combinations of both, for higher-order modes. Radial modes shouldn't happen for devices which are axisymmetric, but they do happen on speaker diaphragms! If you imagine populating the surface of an imaginary speaker with a load of teeny tiny hemispherical radiators - 'monopoles' - you can add up their radiated pressure contribution at some listening position, taking into consideration the phase put in by the different path lengths to the receiver, and the magnitude / phase differences put into each tiny source velocity given by what the modes are doing at that frequency. So what is going on varies considerably as you move off-axis, and this effect gets more extreme the closer you are to the loudspeaker (the so-called 'near-field' - though this is a term which gets abused in all sorts of ways).
Changes in geometry shift the modal frequencies (eigenvalues) and the mode-shapes a little, but they still happen. The other thing you can do is mess around with their Q (by playing with material damping in the cone, and at the surround as already mentioned) and also by messing around with anisotropic cone materials, which is where B&W's interest in woven kevlar came from. That square-weave encourages square modeshapes (at least at low orders), which tend to cancel for on-axis radiation. You can also control the Q with whatever you dope it with.
Perhaps I need to go and lie down. I don't revisit this stuff all that often
