Model for piano hammers: Experimental determination and digital simulation

Abstract

To explain the clearly nonlinear character of the interaction between a piano hammer and the strings it hits, a model for the hammer is proposed consisting of a point mass and a nonlinear, hysteretic spring that describes the action of the felt. Experimental determinations of force are fitted with an expression of generic form F=a(Δy)α, where α takes values such as 2.1, 3.5, and 5. Numerical simulations of hammer and string motions based on this model are found to be in good agreement with experimental measurements.