DYNAMICS OF THE PIANOFORTE STRING AND NARROW HAMMERS

A new method of solution to the equation of a perfectly flexible strin g, when struck at any point by hard or soft narrow hammers, is develop ed. The hard hammer is modeled as a point mass, and the soft hammer is modeled as a point mass backed by a linear or nonlinear spring and a dashpot, representing the compliance and dissipation of the felt. For each hammer the equation describing the string-hammer contact force du ring the periods of contact, and of recontacts, is derived explicitly. The Green's function for a fixed-fixed string is represented by an in finite series of Heaviside functions. The analysis is exact in the spa tial domain thereby eliminating modal truncation error and capturing a ll discontinuities in the contact force. The method predicts the conta ct force and system. response under impacts given any hammer to string mass-ratio that experiences any number of multiple contacts during th e hammer strike.