Scientia Sinica

14 SCIENTIA SINICA Vol, V.

OF O1F BEG na Vt ves OY oo ea oO? | OF OTF —«[@tnvit 6+noe|Se+eS% 0, (2) 2 1 0p Kn OD Viet Ox? 73 Of Oe (73)

From these two equations it can be seen that @ is a wave function, but F, in general, cannot be expressed in terms of wave functions.

VII. PropacaTion oF Waves IN CYLINDER

Consider a transversely isotropic cylinder with planes of isotropy perpendicular to generators. A nondispersive wave is propagated along the cylinder with constant velocity c. In this case, the displacement components have the forms

u=u(x,y,€), v=v(x,y,€),; w=w(x,y,0), (74) where

€=z—ct. G5) Stress functions have the forms F= F(x, y,C), P= P(x, 7,0). (76)

Consequently equations (72) and (73) are reduced to

2 ay Vi F + [y+a B—1—K« c(aty)] Vie + 2 2 4 O"F aA + [By c?(B+y) + Kk? c4] age = 0: (77) 2 VizmiG= OLD) an 7 ViePpt ys al? =0. (78)

Let +5,, +5, be the four roots of the equation ay — [+a B—1—K *aty)] * + [By—K (PHY) +c] t= 0. (79) Then equation (77) can be written in the form

2 1 or) 24,1 0 Vp Vite gen) Yi agen) =o (80)