| Summary: | 博士 === 國立臺灣大學 === 機械工程學研究所 === 106 === In this dissertation, the Mindlin plate theory and high-order shear deformation plate theory are presented and applied to analyzing the flexural and extensional dominated dynamic characteristics for completely free rectangular plates. First, the analytic solution of Mindlin plate theory will be derived. Next, the theoretical analysis and numerical calculation results are compared. In order to solve the vibration problem for engineering application, the Mindlin plate theory is utilized to calculate the reasonant frequencies and mode shapes of piezoelectric plate. The mechanical fields and electrical fields are also presented to design the effective electrodes for excitation. Finally, the high-order shear deformation theory is presented to solve the three-dimensional vibration problem, and the dynamic characteristic of soild is discussed in detail.
First, the Mindlin plate theory is applied to analyze the resonant vibration of a isotropic thick plate. The resonant frequencies and mode shapes of a rectangular thick plate with completely free boundary conditions are analyzed. Three displacements of the flexural mode and extensional mode are presented base on the superposition method. This solution provides the result for the coupling of out-of-plane and in-plane vibrations with the dominated motion of flexural or extensional motion. The solution obtained from this superposition method has excellent convergence for numerical calculation. Furthermore, this method can be easily applied to construct the results for different boundary conditions. From the same way, Mindlin plate theory can be also applied to solving the dynamic characteristic of piezoelectric thick plate. Base on this investigation, the three-dimensional dynamic characteristics and the relation between mechanical fields and electrical fields of piezoelectric material are presented.
The high-order shear deformation theory is derived to have better prediction than Mindlin plate theory for high reasonant frequencies. The high-order displacement assumption and Hamilton’s principle have been used to construct the equation of motions and the boundary conditions. Utilizing the superposition method and Levy solution, the displacement functions can be derived, and the resonant frequencies and corresponding mode shapes could also be obtained. To verify the accuracy of theoretical solution, the resonant frequencies and the corresponding mode shapes are compared with that obtained by FEM calculation. The result of high-order shear deformation theory and FEM are consistent with great accuracy for three-dimensional solids.
Some experimental results are used to verify the accuracy of Mindlin plate theory and high-order shear deformation theory. First, the full-field optical technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is utilized to get the resonant frequencies and corresponding mode shapes to comfirm the accuracy of the results by Mindlin plate theory. To excite the thick plate resonant frequency, we use free fall steel ball to impact the thick plate to generate the transient time response. By using Fast Fourier Transform of the time response, the resonant frequencies can be obtained. From the comparison result of theoretical analysis and experimental measurement, the analytical results obtained in this study can be used to determine the mode shapes and resonant frequencies of the thick plate with good accuracy.
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