梯形壓電陶瓷平板振動之理論與數值探討

Theoretical and Numerical Investigations for the Free Vibation of Piezoceramic Trapezoidal Plates

柯典志(Tien-Chih Ke)

指導教授 ： 黃吉宏

健行科技大學/工學院/機械工程所/碩士(2009年)

https://doi.org/10.6824/UCH.2009.00015

摘要

本文主要應用立茲法(Ritz’s method)與pb-2形函數(pb-2 shape functions)結合等效常數之引用，以求出梯形壓電陶瓷平板在不同邊界條件下之側向振動特性。所謂等效常數是藉由比較等向性及壓電陶瓷平板之振頻特徵方程式，進而推得之等效蒲松比及等效彎曲剛度常數。在數值分析方面，則是藉由有限元素分析軟體進行振型及振頻之計算，以便與理論分析結果做比較，結果顯示兩者具有相當好之一致性。最後亦將針對梯形壓電陶瓷平板於單邊固定及四邊固定之邊界條件下，因幾何形狀(錐度比及傾斜角)之變化，對平板共振行為之影響，作一分析與討論。

關鍵字

梯形壓電陶瓷平板 ； 振動 ； 立茲法 ； 等效常數

並列摘要

By using the Ritz’s method and pb-2 shape functions incorporated with the equivalent constants, the transverse vibration of piezoceramic trapezoidal plates are discussed with various taper ratios and sweep-back angles. By comparing the characteristic equations of resonant frequencies between isotropic and piezoceramic disk, the equivalent Poisson’s and equivalent bending stiffness are derived and then the resonant frequencies of transverse vibration can be obtained for piezoceramic plates. Numerical results obtained by finite element method(FEM) are employed to validate the theoretical results for different boundary conditions. It is shown that the theoretical predictions of resonant frequencies and the corresponding mode shapes agree well with numerical results. The influences of taper ratios and sweep-back angles on the vibration behavior of clamped-free-free-free(CFFF)and clamped-clamped-clamped-clamped (CCCC)trapezoidal plates are also demonstrated in terms of the dimensionless frequency parameter.

並列關鍵字

piezoceramic trapezoidal plates ； vibration ； equivalent constants

參考文獻

[1] 黃吉宏，「應用振幅變動電子斑點干涉術探討三維壓電材料體及含裂紋板的振動問題」，台灣大學，博士論文，民國八十七年。

[2] 徐千享，「含裂紋梯形平板振動特性分析與實驗量測」，清雲科技大學，碩士論文，民國九十三年。

[3] 陳逸裕，「應用立茲法探討壓電陶瓷平板之側向振動特性」，清雲科技大學，碩士論文，民國九十四年。

[4] Adelman, N.T and Stavsky, Y., “Axisymmetric Vibration of Radially Polarized Piezoelectric Ceramic Cylinders”, Journal of Sound and Vibration, 38(2), 245-254 (1975).

[5] Adelman, N.T and Stavsky, Y., “Vibration of Radially Polarized Composite PiezoelectricCylinders and Disks”, Journal of Sound and Vibration, 43(1), 37-44 (1975).