Scientia Sinica

No. 1

This system is simpler than (15) in form.

HU: EQUILIBRIUM & VIBRATION OF TRANSVERSELY ISOTROPIC ELASTIC BODY 5

Consider, as an example, an infinite space under a concentrated force P.. By taking the point of application of the force as the origin of the co-

ordinate axes, we have

3

By Ba 4n) V x2 Ey? +s? 2? For the sake of simplicity, let us write

eae Sy = 5,25 Gy = Oo Then expression (19) can be written in the form

Bis et ee nD)

GG ve) Gay) By By 4 V 7? 3?

Substituting this expression into equations (18), we have

op 23, Pet f on \ . By By 4% vy liv 2423 52V pt z3 J”

o7F _ By . Pe . iL | Sy a... S52 Oz? By Big 4 Vi — V2 LW Peet VV 83

Integrating equation (22b) twice with respect to 2, we have

r== By3 _ Ps 1 \ V 222

2 op By, By, 4 vi—V2 V x3

Bi, Ps Si @Si,2a)s Coa)

(20)

(21)

(22a)

(22b)

(23)

It may be verified that this expression satisfies equation (22a). Therefore it is the required solution. Substituting expression (23) into formula (8), we

obtain By3

Re it | 24 Zo \ x ee . : _ = 2 By Ba, 4m vy—v2 |W 42t V P23) 7

(24)

By; ; Pz . 1 | zy a 22 , vy

By, Bag 4 V1 —v2 V +23 V Pee ie

= 1 _P: 1 = 83 Bys—Bur By Bag 4% v1 —¥2

3 V Pts VW Pte

>

\.

These expressions coinside with that obtained by H. A. Elliot".