Scientia Sinica

No. 1 HU: EQUILIBRIUM & VIBRATION OF TRANSVERSELY ISOTROPIC ELASTIC BODY 7

where

ee . _—— oo (31)

In general, a special solution may be obtained in the following manner. Let

(y it eae =) (93 +33 -)H= Jo(#3y, 2).

1 Oo 1 Oo (Up ae) it Gy ge) Be he. (32) (vitae rit = Ii(x.y,2). 50 ST Equation (27) is reduced to the form Chip Challe GRE Bis = aw tf Oy? F Oz? ~~ By Bay Bos xX, Gs ils; As (33)

As in the last section, in order to obtain a special solution, we may consider the body to be an infinite space. Then from equation (33) we have

oe oe X(E, 7,6) dé dy de TiC: HE) a is. Bee aa Nea SS i

C=Opy 5) 5 (34)

After having determined J;, we may obtain H by integrating (32). System (32) may be written in the form

3 07H o*tH Viet + (y+ 2) Vi pet + 1254 = Jo> A wel ViH + (t+) vise + v2» SS ie (35)

el ViH + (vy +0) VISE a + vo 1 ~ =).

4 Regarding viH, vi on , —

these unknowns from system (35), we get

as three algebraic unknowns and solving

ee vi(vi— v2) Jo-Evi(va—vo) Ji tv3(vo—1) Jo (36a) : (v9—v1) (v1 v2) (v2—v9 ) ° v7 0 — Y%(vi=v2) Jo#vi(v2—v9) Jy v2(vo— 1) Ja (36b)

1 Oz? (vo— 1) (v1 2) (v2 V9)