Vibration modal analysis of resonance board of Pi-pa.

As one of the most important components, the resonance board affects largely the acoustical quality of musical instruments. In this paper, the resonance frequencies in 0-1 000 Hz of Pi-pas top resonance board made by Paulownia elongata were measured by FFT analyzer in the boundary conditions of cantilever. Resonance frequencies of some modes were identified easily,such as 28.75 Hz (0,1), 87.50 Hz (1,0), 171.25 Hz (1,1), 177.50 Hz (0,2), 295.00 Hz (2,0), 372.50 Hz (2,1), 395.00 Hz (1,2), 488.75 Hz (1,3), 581.25 Hz (3,0), 661.25 Hz (2,2), 688.75 Hz (2,3), 788.75 Hz (3,2), 856.25 Hz (1,4) and 957.50 Hz (4,0), but some were identified difficultly, such as (0,3), (0,4), (3,1), (4,1), etc. Then the vibration modes corresponding to all resonance frequencies were analyzed. Three kinds of vibrations including bending vibrations in longitudinal and transverse direction of wood grain and torsion vibration were driven after the resonance board was rapped. The torsion vibration mode is not an exact sum of bending vibrations in longitudinal and transverse directions. The vibration mode is nearly symmetrical along longitudinal axis of wood grain, but is not completely symmetrical along transverse axis. This is attributable to the pearshape of Pi-pas resonance board. The resonance frequency has similar variation trend for (0,n), (1,n), (2,n) and (3,n) with n increasing.