《弹性力学》（双语版） 第十一章 弹性波

Plastics wave Because of the equilibrium relations we simplify them and x+++X一2=0 Cx OyO at 0(xO 0 0z ax +-P=2 01y Z-p2=0 Ox ay at The above formulas are called movement differential equations of elastic objects. They and geometry equations and physIc equations are the basic equations of movement questions of elasticity mechanics

11 Because of the equilibrium relations ,we simplify them and get: The above formulas are called movement differential equations of elastic objects. They and geometry equations and physic equations are the basic equations of movement questions of elasticity mechanics 0 2 2 =   + −   +   +   t u X x y z x yx zx     0 2 2 =   + −   +   +   t Y y z x y z y xy      0 2 2 =   + −   +   +   t w Z z x y xz yz z    

弹篮波 由平衡关系,并简化后得: 00x++0+X-Pan2 07a o u 0 Ox Oy az Otx+y -Y-p- 0 az ax at 00 ar ar 2z+z-p 0 az Ox oy at 上式称为弹性体的运动微分方程。它同几何方程和物理方程 起构成弹性力学动力问题的基本方程。 12

12 由平衡关系，并简化后得： 上式称为弹性体的运动微分方程。它同几何方程和物理方程 一起构成弹性力学动力问题的基本方程。 0 2 2 =   + −   +   +   t u X x y z x yx zx     0 2 2 =   + −   +   +   t Y y z x y z y xy      0 2 2 =   + −   +   +   t w Z z x y xz yz z    

Plastics wave Note l: geometry equations Ow Ov ax yy yaz av au: aw y az a av a E.= az ax a 13

13 Note 1: geometry equations: x u x    = y y   =   z w z    = y z w yz   +   =   x w z u zx   +    = y u x xy   +   =  

弹篮波 注1:几何方程 Ow Ov ax yy yaz av au: aw y az a av a E.= az ax a 14

14 注1：几何方程 x u x    = y y   =   z w z    = y z w yz   +   =   x w z u zx   +    = y u x xy   +   =  

Plastics wave Note2: physic equations lox-从(,+0:)yp= 2(1+) 8= E E E,=[,-(0:+01 2(1+p E y E 6:=l:-以(O+0, 2(1+) E E 15

15 Note2: physic equations [ ( )] 1 x x y z E  =  −   + [ ( )] 1 y y z x E  =  −   + [ ( )] 1 z z x y E  =  −   + yz yz E    2(1+ ) = zx zx E    2(1+ ) = xy xy E    2(1+ ) =