I'm currently building a music instrument (string instrument), and I am at the step where one applies certain braces to the soundboard. Since I actually don't know how the bracing will affect the sound (or basically anything) I thought it would be a good starting point to model the soundboard and the applied braces with CAD, and then apply an FEM simulation that will show to me the effect of the braces.
To my Background, I'm a physicist, but besides a course in technical mechanics 1 (statics), and some time selfstudying continuum-mechanics and the cauchy-stress-tensor, I don't have a background in engineering.
The program I'm using can perform a modal analysis on the soundboard, and modal analyses are also is the predominantly used way to model e.g. violin bodys with FEM technology (for example in this publication]1, or in this youtube video).
But of what worth are those simulations actually? In the end, I roughly want to know how well the soundboard is able to transmit frequencies to the air that have been present in the strings before, that means how well an amplitude in a frequency in the strings will translate to an amplitude in air.
A modal analysis will show me in what ways (and with what frequencies) the body will vibrate on its own (without external force applied). But it won't show me the amplitude of the soundboard (because it's abitrary): following (this stack exchange answer on modal analysis, the amplitudes of the eigenmodes can have any value, similar to the length of an eigenvector that also can have any value.
Granted, a periodic force will excite a vibrational modes amplitude the more if it meets its frequency, but doesn't it also play a role where this force is applied? When I apply period forces at a point on the soundboard where a certain mode of that soundboard has a node, I would expect the mode not to be excited at all for example.
Additionally, I know from a simple harmonic oscillator that its amplitude, subject to an external driving force, will reach the maximum at its resonance frequency. Is the same true here? When I apply a driving force to the soundboard, will it be sufficient to check how it affects the eigenmodes of the soundboard, because this will be the strongest excitations anyway?
As an addendum, I am aware that I don't model the transfer from soundboard to air at all. For now, I only want to model the transfer from amplitudes in the strings to amplitudes in the soundboards vibrations.
So to make the question short and concise: What can (and what can't) modal analysis tell me about the transfer of periodic motion from the bridge (where the strings are attached) to the soundboard? And since this information alone is probably not enough - When modelling the effect of external forces on the soundboard, will it be enough to only look at the frequencies of the previously found out eigenmodes?