Sparse Grid Application in the Stochastic Physics-based Model of the Piano Soundboard
* Presenting author
Soundboard is a key element in piano sound production, both its geometry and material selection are important factors. Traditional soundboards are built from solid high quality music wood, but in many instruments wood-laminates or composite soundboards are installed instead. In both cases, parameter variability – resulting either from natural wood characteristics or manufacturing tolerances – plays an important role in the instrument’s desig. In composite laminates both the fibre direction and layer thickness vary, that introduces uncertainty in the soundboard mechanics. We have developed a stochastic finite element model of the laminated piano soundboard that handles uncertain fibre direction and soundboard thickness. The nonlinear relationship between uncertain parameters and the response are modelled using a collocational polynomial chaos expansion technique. We examine the application of sparse grid methods–depending on modelling dimension and nonlinearities–instead of Monte Carlo simulation technique, to compute the uncertain eigenfrequencies and mode shapes of laminated piano soundboards.