琵琶共鸣面板的振动模态分析

Vibration modal analysis of resonance board of Pi-pa.

为研究琵琶共鸣面板的声学振动性能,采用快速傅里叶变换频谱分析仪测定了共鸣面板在0～1000Hz频率范围内的各阶振动频率,并分析了各阶振动频率对应的振动模态。结果表明:共鸣面板的振动可以分成顺纹理方向弯曲振动、横纹理方向弯曲振动、顺纹理与横纹理方向弯曲振动叠加而成的扭转振动3种,但扭转振动的振型并不是简单地由2个方向的弯曲振动叠加而成;各阶振动振型基本呈y轴(顺纹理方向)对称,但并不完全呈x轴(横纹理方向)对称,这主要是由琵琶共鸣面板的仿梨形结构决定的;对于(0,n)、(1,n)、(2,n)、(3,n)的各阶频率,当n值由0逐步增大时,共振频率的变化具有相似的增长趋势。

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 cantilever. Resonance frequencies of some modes were identified easily, such as 28.75 Hz nz （1,0）, 171.25 nz （1,1）, 177.50 Hz （0,2）, 295.00 Hz （2,0）, 372.50 Hz （2,1 （ ） conditions of 0,1）, 87.50 , 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.