Analysis Of Static And Dynamic Response For Guzheng Top Plate Under String Loading

The soundboard is an essential part of a wooden instrument,and the vibration characteristics and mechanical properties of the soundboard are important factors affecting its acoustic quality.Due to the special structure of wood,the resonant body or the top plate of a wooden instrument will be subjected to complex stresses under the string force loading,which will lead to the change of stiffness and small deformation,resulting in its resonant frequency and vibration mode different from the original condition,and the final response effect will be affected.This study takes the frame Guzheng top plate made of paulownia as the research object,analyzes the influence of the thickness and arch height of the Guzheng top plate on its vibration mode;analyzes the static response of the top under different string force conditions,and explores the inner connection between deformation and stress response,mechanical factors and thickness distribution;explores the applicability of the analysis of the vibration signal of the top plate based on the fast Fourier transform and Hilbert-Huang transform.The strain response law of the top plate under the action of string excitation force at a specific frequency is also analyzed.The main results of this study are as follows:(1)The vibration mode of the Guzheng top plate was investigated by means of experiments and finite elements,and the reasonableness of the Guzheng simulation model and its parameters established in this study were compared and verified,and the influence of the thickness and arch height of the top plate on its resonance frequency and static response of each order was analysed.It is found that the thickness of the Guzheng top plate is reduced from11 mm to 7 mm and the arch is reduced from "45 mm at the beginning to 32 mm at the end" to "35 mm at the beginning to 25 mm at the end",which is conducive to a lower resonance frequency of the Guzheng top plate as a whole.and obtain a better low-frequency response,and to enhance the sound function radiation of the Guzheng in the low frequency range.In a series of top plate models in this study,the thickness configuration of 10 mm thick in the middle register,9 mm thick in the bass register and 8 mm thick in the treble register can suppress the deformation of the Guzheng top plate under static tension more effectively,which facilitates the luthier to consider the structural bearing capacity and low-frequency response ability of the top plate when determining the thickness parameters of the Guzheng top plate,so as to produce the Guzheng with ideal mechanical properties and acoustic quality and avoid blindness.(2)By applying the finite element method,the string component forces acting on the top plate through various paths were applied to the corresponding positions,and the displacement,stress and strain fields in all directions of the top plate were calculated and their patterns were investigated to analyse the structural response of the Guzheng top plate under this static load.It is found that when the string tensions from 16 to 21 are withdrawn,the peak deformation in the length direction of the top plate is reduced by 53.55% and the peak stress is reduced by 55.08%,and the peak deformation in the thickness direction of the top plate is reduced by 43.10% and the peak stress is reduced by 72.54%,which effectively suppresses the dynamic response of the top plate and the response in the stress area is more evenly distributed.It shows that by assembling the reinforcement plate to share the load transferred by the higher string force,the in-plane shear stress of the Guzheng top plate can be effectively reduced,and its dimensional stability can be enhanced to achieve higher load-bearing capacity and prolong the life of the Guzheng.(3)Signal processing methods based on Fast Fourier Transform and Hilbert-Huang Transform were used to analyze the data,which are verified by finite element analysis,proving that for the Guzheng top plate vibration signal whose frequency components change with time,the signal processing based on the fast Fourier transform cannot accurately analyze the influence of each string force on each order frequency of the top plate,while the Hilbert-Huang transform method can adaptively decompose the original signal into the signal of a single frequency component,and by selecting the target frequency component for time-frequency analysis,it can to a certain extent attenuate the modal confusion,and can capture the small changes of transient frequency of the top plate under different working conditions,which has better applicability.The results can provide some new ideas for the extraction and analysis of vibration signals of musical instrument soundboards.(4)Harmonic response analysis was used to predict the stress response conditions under the action of excitation forces at different frequencies,and strain measurements and transient response analysis were carried out to obtain the strain response of the top plate under the action of excitation forces at various frequencies.It is proved that when the fundamental frequency of string vibration is close to the resonance frequency of the Guzheng top,the resonance of the top is strengthened and the strain response is increased by about 2.64 times.The result has some scientific reference significance to the selection of material for the production and performance improvement of the Guzheng top plate: the difficulty of reducing the supply of raw materials is alleviated by changing the parameters of the wood for the resonant top plate that does not meet the requirements in order to adjust its resonance effect at a certain frequency,instead of discarding it directly.