To address the pollution issues of industrial oily wastewater and catering industry wastewater, a series of Ti₃C₂T_x/TEMPO oxidized cellulose nanofibers composite aerogels with varying Ti₃C₂T_x content were successfully prepared using liquid nitrogen non-directional and directional freezing methods, with Ti₃C₂T_x and TEMPO oxidized cellulose nanofibers (TOCNF) as the main raw materials. The prepared samples were then hydrophobically modified using methyltrichlorosilane (MTCS) via chemical vapor deposition (CVD). The results showed that the directional Ti₃C₂T_x/TOCNF composite aerogel had the most orderly SEM morphology. The hydrophobic Ti₃C₂T_x/TOCNF composite aerogels exhibited efficient adsorption separation capabilities, with an adsorption capacity ranging from 21.5 to 78.2 times their own mass. Notably, the oil absorption performance was optimal when the mass fraction of Ti₃C₂T_x was 33.3%. After five adsorption cycles, the adsorption capacity of M5C10 (with a mass ratio of Ti₃C₂T_x to TOCNF of 5:10) only decreased by around 11%. M5C10 exhibits highly efficient oil absorption performance, which is of considerable significance for the research on oil-water separation treatment of industrial wastewater, domestic wastewater, and sewage from the catering industry.

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.