Abstract
In this paper, the vibration system of a piano string and a sound board (Fig. 1) is analyzed by the finite element method (Fig. 2). The string is stretched with constant tension P between the upper bearing and the lower bearing, and is assumed to be completely flexible. The mass point m are distributed along the string at equal distances, and m_1 indicates the upper bearing, m_<103> the lower bearing, m_<97> the equlivalent mass of the sound board, and k the spring constant. It is also assumed that the mass-point of the hammer m_H collides with the point m_N on the string with an initial velocity x^^^. _H, that they repel each other according to Newton's law, and that m_N is decelerated by the tension P. Then it collides with m_H again, and this series of motions is repeated. These motions of all points m_i, m_H, m_N are expressed by Eqs. (1), (2), and (3). The flow diagram of the program is shown in Fig. 6. The calculated values by this simulation program and the measured values of an actual piano are presented in Figs. 7 and 8. Comparisons between them show good agreement.
