拼板结构的古筝共鸣面板振动模态研究

  目的  古筝共鸣面板的结构是影响其振动性能的重要因素之一，不同结构的共鸣面板发出的音质与音色会有所差异，迄今很少有学者就拼板古筝共鸣面板的振动发声特点展开研究。  方法  本研究以拼板古筝共鸣面板为研究对象，利用两种模态分析方法探讨其声学振动性能。采用实验模态分析法，运用数字信号处理技术对采集到的激励力信号和振动响应信号进行分析，经过数据转换求得系统的频响函数，进而得出各阶次共振频率及其对应模态振型；采用计算模态分析法，建立拼板结构共鸣面板的三维模型，运用有限元法对其进行离散，通过近似方法求解出各阶次共振频率及其对应模态振型。  结果  实验模态结果显示:拼板共鸣面板能够识别到的阶次有(0, n)和(1, n)阶，且多集中在(0, n)阶，(1, 4)、(1, 6)、(1, 7)和(1, 10)阶为沿横纹理方向和顺纹理方向弯曲振动叠加的复合振动，识别较困难。从振型上看，拼板共鸣面板各阶的模态振型相对清晰易识别。与实验模态结果相比，计算模态分析能够识别到选定阶次范围的所有阶次，所得振型图更加均匀且理想，而实验模态分析时个别阶次较难识别。拼板共鸣面板计算模态结果与实验模态结果呈显著的线性相关性，相关系数为0.999 6。  结论  从模态分析结果来看，相对整板结构，拼板共鸣面板各阶共振频率对应的模态振型整体清晰易识别，振动频率更高；从木材利用率方面来讲，相对于制作整板，拼板共鸣面板更有利于节约木材资源。通过两种模态分析结果综合对比，验证了计算模态分析应用于拼板结构古筝共鸣面板的振动模态研究具有可行性。 

Vibration mode of Guzheng soundboard with composite structure

  Objective  The structure of the Guzheng soundboard is one of the important factors affecting its vibration performance. The sound quality and tone color of the soundboards with different structures will be different. So far few scholars have studied the vibration and sound characteristics of the common structure of the composite Guzheng soundboard.  Method  In this study, two modal analysis methods were used to investigate the acoustic vibration performance of the composite soundboard. The experimental modal analysis method was used to analyze the collected excitation signal and the vibration response signal using digital signal processing technology. After data conversion, the frequency response function of the system was obtained, and then the resonance frequencies of each order and the corresponding modal shapes were obtained. Through using computational modal analysis, a three-dimensional model of the composite soundboard was established, discreting it by finite element method, then the resonance frequencies of each order and the corresponding mode shapes were calculated by approximate method.   Result  The experimental modal results showed that the (0, n) and (1, n) orders could be identified and they were mostly concentrated in (0, n). The (1, 4), (1, 6), (1, 7) and (1, 10) order were composite vibrations that bending along grain and perpendicular grain directions, and they were more difficult to identify. The modal shapes of the composite soundboard corresponding to each order frequency were clear and easy to identify. Compared with the experimental results, the computational modal analysis could identify all orders in the selected order range, and the modal shapes were more uniform and ideal. However, it was difficult to identify individual orders in the experimental modal analysis. The results of computational modal analysis showed significant linear correlation with the experimental modal results, and the correlation coefficient was 0.9996.   Conclusion  From the results of modal analysis, the modal shapes of the composite soundboard corresponding to each order frequency are easier and more clear to identify than the whole soundboard, and the vibration frequency is also higher. In terms of wood utilization, the composite soundboard is more conducive to saving wood resources than making the whole soundboard. Through the comprehensive comparison of the two kinds of modal analysis results, it is verified that the computational modal analysis is feasible to apply to the vibration modal analysis of the Guzheng soundboard.