Piano string excitation. VI: Nonlinear modeling
Donald Elliott Hall · The Journal of the Acoustical Society of America · 1992
Accurate modeling of the piano string–hammer interaction requires that the nonlinearity of the force-displacement relation for the hammer be recognized and included. Two models that accomplish this with numerical integration are described, and sample results are presented. The first model is valid for a perfectly flexible string, where nondispersive traveling waves can be conveniently followed with a digital delay line. The second model uses standing waves instead to describe the vibrations of a stiff string, with the stiffness itself justifying truncation of what would otherwise be a poorly converging normal-mode summation. Predictions with these models give significantly better agreement with data than did previous calculations with completely linear models.