Experiments and Simulation on the Effects of Arch Height Variation on the Vibrational Response of Paulownia Wood

Resonance boards of Chinese traditional instruments such as the Guzheng and Guqin typically are arched, with the arch height influencing their resonance characteristics. This study focuses on Paulownia wood utilized for resonance boards. The bottom surfaces were thinned in 1 mm increments, with vibration signatures acquired at each reduction stage using a multi-channel FFT analyzer. Subsequently, time-domain characteristic parameters of the signals were extracted through MATLAB-based signal processing. Modal and harmonic response simulations of the structure were conducted using finite element software. The results indicated that variations in arch height affected the frequency spectrum response of the vibrations of Paulownia wood, altering the structural energy radiation levels. Lower arch heights (0–2 mm) had a greater impact on the fundamental frequency. The arch height was 1 mm and 2 mm, with R1,1 and R1,2 being −5.31% and −8.62%, respectively. Skewness and kurtosis were negatively correlated with arch height. When ΔH was 3.06, the radiation effect was optimal. The changes in arch height influenced the vibrational modes and energy distribution of Paulownia. Higher arch heights (3–6 mm) have less effect on the fundamental frequency and impose some constraints on the mode vibration pattern. Furthermore, the results of the frequency-domain and time-domain analyses were found to be largely consistent with the finite element simulation results. The results provide guidance for changing the arch height to modulate the acoustic vibration response of the resonance board, which is of significance for the personalized design of future musical instruments.