| Summary: | 碩士 === 國立交通大學 === 理學院應用科技學程 === 102 === This thesis propose a method to rapidly and accurately reconstruct the resonant modes and dispersion relationships of thin plates in different materials. In the past, the reconstructions of resonant modes are usually fulfilled by utilizing some approximative method based on numerical iteration to match the experimental resonant frequency spectrum. Besides, the measurements of key elastic coefficients of material, e.g. the Young’s modulus and Poisson ratio, are necessary for the determination of acoustic dispersion relationship. However, not only the numerically iterative process requires tedious calculations which takes lots of time, but the precision of elastic coefficients depend on a large amount of statistics on experimental data. As a consequence, rapid analysis of resonant modes and dispersion relationship are hard to achieve case-by-case by the traditional method. In this work, we analytically develop a theoretical model to calculate the Chladni figures of thin plates. We show the experimental resonant modes can be perfectly reconstructed once the theoretical nodal patterns reveal one-to-one correspondence to the experimental observations. We further demonstrate the dispersion relationships of thin plates in different materials such as aluminum, brass, copper, stainless steel, glass, wood and PMMA can be easily determined by linking the resonant frequencies to the reconstructed wavenumbers.
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