1. 三維壓電彈性力學 Chien-Ching Ma Ru-Li Lin 92.03.31

2. 內容大綱 三維問題 二維問題 _ 平面問題 二維問題 _ 反平面問題 二維問題 _ 壓電問題 二維問題 _ 解的架構 二維問題 _ 全平面的基本解 二維問題 _ 半平面的解函數

3. 三 維 ( 3 – D ) 問 題 二 維 ( 2 – D ) 問 題 平 面 問 題反 平 面 問 題平 面 問 題反 平 面 問 題

4. Constitutive Equation of Piezoelectric Material : 電位移 (Electric displacement) : 電場 (Electric field) : 彈性模數 (Elastic modulus) : 壓電係數 (Piezoelectric coefficient) : 介電常數 (Dielectric constant) : 彈性柔度 (Elastic compliance) : 壓電常數 (Piezoelectric constant) : 反誘電常數 (Dielectric impermeability constant)

5. 構 造 方 程 式 的 矩 陣 形 式

6. Generalized Plane Problem (infinite at z)

7. Equilibrium Equations : Elastic Equilibrium, (f i : body force) : Gauss’s law of Electrostatics or Maxwell’s equation (q: electric charge density) Compatibility Equations

8. Stress and Electric Displacement function (,, ) In-PlaneAnti-PlaneIn-Plane

9. Governing Equation of Generalized Plane Problem

10. Special Cases Case I : Monoclinic (symmetric w.r.t. x-y plane, class m) In-plane problem of piezoelectric material

11. Case II : Transversely Isotropic (Hexagonal, class 6mm) Anti-plane problem of piezoelectric material

12. Case III : Orthotropic (Orthorhombic, class mmm) Case IV : Orthotropic (Principal axis = axis of coordinate ) No piezoelectric effect

13. Plane problem of transversely isotropic material Symmetric plane = x-y plane, poling direction = z axis

14. Complete State of Electromechanical Interaction for Two-Dimensional Model

15. Constitutive Equations of Two-Dimension Transversely isotropic material

16. Equilibrium equation (absence of body force and free electric volume charge) Compatibility equation Stress function and electric displacement function

17. Governing Equations of Two-Dimension Transversely isotropic material

18. Explicit form of governing equation Fourier transform pair

19. Governing equation in transform domain Let Characteristic of roots (form I) Characteristic of roots (form II)

20. Operator in transform domain Let where By Or where Relations of and in the transform domain

21. Field in the transform domain

22. General solution in the transform domain

23. Green’s Function of Infinite Plane

25. Surface Green’s Function of Half-Plane