彈性支撐壓電複合層板之非線性振動分析

Nonlinear Vibrations of Piezoelectric Composite Plates with Elastically Restrained Boundary Conditions

李佩君(Pei-Chun Li)

指導教授 ： 葉豐輝

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00286

摘要

本文係研究彈性支撐壓電複合層板之非線性振動分析。首先採用簡單高階剪變形理論，配合Von Karman大變形理論和壓電理論，利用漢姆頓定理（Hamilton’s Principle）和變分法推導出壓電複合層板之統御方程式，並利用雙重傅利葉級數（Double Fourier Series），推導出一組非線性代數方程組，然後利用Ritz Method求得非線性頻率解。 本文詳細探討不同振幅、不同長寬比、材料厚度、壓電材料疊層角度、邊界彈性係數等參數對非線性頻率的影響，所得部分結果與文獻比較十分吻合，可證實本文分析結果應屬正確，可提供壓電複合層板非線性振動分析參考之用。

關鍵字

壓電複合層板 ； 非線性振動 ； 彈性支撐

並列摘要

The thesis studies the nonlinear vibrations of piezoelectric composite plates with elastically restrained boundary conditions. Based on the simple high-order theory, von Karman theory, and piezoelectric theory, the equations of motion for piezoelectric composite plates are derived by Hamilton’s principle and variational principle. Generalized double Fourier series are used to constitute a set of simultaneous algebraic nonlinear equations, and then the nonlinear frequencies are solved by Ritz method.
The influences of aspect ratio, thickness-to-length, angle of orientation, elastically restrained coefficients on nonlinear frequencies are particularly discussed in this thesis. A good agreement is obtained from the comparison of some special results between the thesis and literatures. It is proved that the results are correct in this thesis, and should serve as references for nonlinear vibration analysis of piezoelectric composite plates.

並列關鍵字

piezoelectric composites plates ； nonlinear vibration ； elastically restrained

參考文獻

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5. Z. Ding, Y. K. Cheung, F. T. K. Au and S. H. Lo, “Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method,” International Journal of Solids and Structures, Vol. 39, pp.6339-6353 (2002).

6. P. Heyliger and D. A. Saravanos, “Exact free-vibration analysis of laminated plates with embedded piezoelectric layers,” Acoustical Society of America, Vol. 98, pp.1547-1557 (1995).