Experimentally-tuned Synthesis Of A Thin Plate

The numerical simulation of acoustic instruments and devices is a growing subject of research. Applications range from model-aided instrument making, to virtual instrument and effect design, to virtual reality applications. A faithful reproduction of the underlying system may be realised via signal-based analysis and resynthesis, starting usually from a recorded sample. Model-based synthesis, on the other hand, allows to reproduce the dynamics of common objects such as strings, bars and plates by setting a few physically meaningful parameters feeding a mathematical model. The latter allows far greater flexibility in terms of control and design, but often lacks the realism of the former. This work investigates the possibility of tuning a physical model using experimental data. The system considered here is a cantilever metal plate struck with a hammer. The physical model is derived from a modal decomposition of the Kirchhoff plate equation. A preliminary estimate of the unknown plate's rigidity constant is carried out first, via the measurement of the first eigenfrequency. Then, the finite difference scheme is used to solve the eigenvalue problem over a fine grid with the computed rigidity constant, and the modal shapes are then stored along with the modal frequencies. Experimental data are collected from a laboratory experiment, and a comparison of the experimental frequencies against the model's eigenfrequencies is carried out. The modal equations obtained from the difference scheme are then adjusted to compensate for the errors in the eigenfrequencies. Experimental decay times are also implemented in the scheme. Tuned numerical impulse responses at three different combinations of input and output locations are then computed and compared to the experimental responses, showing a high degree of accuracy.