The title is just a tad misleading. There is no such structure that’s "Resonance Free". If a structure has mass and stiffness associated with it, there are resonant frequencies. You may have pushed it out of the sub’s operational range or not (test or sim tool could let you know), but, there are some resonances around..
You can either dump your CAD and material properties for the wood (modulus, poisson’s ratio, etc) in some FEA tool and all resonant frequencies can be computed. You will need to know how to work with FEA tools in this case.
Or get a DAQ and a couple of accelerometers... Start sweeping the driver and determine if any resonances can be caught (coarse). You will need to know some basics of signal processing in this case..