Analysis of Vibration and Mechanical Properties of Soundboards Based on Thin Plate Theory

In order to optimize the material selection and structure in the design of musical instruments, the vibration characteristics of a rectangular soundboard are modeled and simulated based on the thin plate vibration theory. Firstly, the geometrical dimensions (length, width and thickness) of the soundboard are set as the basic parameters, and the vibration model is constructed to derive the partial differential equations. After simplifying the equations by the method of separating variables, the finite difference method was utilized to solve the equations in Matlab to obtain the first few orders of the modal vibration pattern images, and the first three orders of the intrinsic frequency data were extracted. In order to study the material effects, four typical materials were selected, and polynomials were fitted to the frequency data with the help of numpy, matplotlib and scipy libraries in Python to obtain the expressions of vibration equations. The results show that the material properties (e.g., modulus of elasticity, density and Poisson's ratio) have a significant effect on the vibration frequencies and modes, which provides theoretical support for the design of musical instruments.