A model analysis of force-deformation characteristics of a piano hammer
Hideo Suzuki · The Journal of the Acoustical Society of America · 1988
Effects of a geometry and a Young's modulus profile of a piano hammer on its static force-deformation characteristics are studied using a finite element mode. The material properties of the model are assumed to be linear as well as isotropic. Therefore, only a geometric nonlinearity is considered. A hammer model with a representative geometry and Young's modulus profile of an actual bass hammer has a force (f)-deformation (d) relationship approximated by a function, f = AdB , with approximately B = 1.7. On the other hand, the degree of nonlinearity (B) of a particular hammer obtained from a dynamic measurement is approximately 2.3 or larger. A hammer with a larger increase of Young's modulus in the inward direction has a larger degree of nonlinearity. The geometry of a hammer has a large effect on the value A in the formula shown above. A hammer with a shorter height (distance from the top of the hammer to the top of the wood piece) or with a larger width has a larger value of A (in other words, a larger stiffness).