Towards better copies of guitars: Compensate material variability with geometry

Luthiers have been trying to copy the sound of iconic instruments like Torres guitars for many years. Though precise geometric copies were manufactured, audible differences were found which can be attributed largely to the natural variability of wood. We were able to present a methodology allowing non-destructive material identification based on which a shape optimization was performed to compensate material variablility with specific geometric variations, allowing a much more exact copy of a guitar soundboard in terms of eigenfrequencies. We will present a generalization of this methodology to full guitars including almost arbitrary geometric adaptions and consideration of mode shapes in the optimization. A mesh morphing strategy allows to simultaneously define very general geometric adaptions and comparing mode shapes without re-meshing. Further, a parameterized reduced order numerical model will be presented in which all possible global geometric variations are mapped to the individual elements of the underlying finite-element model in symbolical form. This symbolical representation is then carried over to the assembled finite-element matrices resulting in an extremely efficient reduced model keeping the symbolic relationships. This is the absolute core requirement of an efficient shape optimization. The approach will be presented for hexahedral elements.