Scientia Sinica

No. 1 HU: EQUILIBRIUM « VIBRATION OF TRANSVERSELY ISOTROPIC ELASTIC BODY 17

P=0, F=F(r, x2). ey Xs) Consequently we have

OF

Of Oe! Or Oz’

oz? 2

w=aViF+y (97)

tg=O0, “=

The stress function F satisfies equation (72), where the differential operator Vv? is reduced to 1.0 9

r

r Or Or

(98)

2 Wire In general F is not expressible in terms of wave functions.

4

3. Flexural vibration. In the case of flexural vibration, we can put neither F nor @ equal to zero. But as for the static problem, here we may assume that F and @ have the following forms

F=f (1, 2,2) cos0, =, 2,2) sind. (99)

Consequently in this case #,, wW, %,, 99, =, T-; are proportional to cos@ and ue, Te, 7, are proportional to sin @.

REFERENCES

[1] Jlexaumxa, C. T., 1940. Cmwmerpausad mecdopmalua u KpyyeHue Tella BpauleHHA C aHH30TpONHMel yacTHoro Buna. [puxa. Mam. Mew., 4.

[2] Jlexaumxait, C. T., 1950. Teopua ynpyocmu anusomponnoro mesa. ToetTexu3yar.

[3] Moisil, A., 1950. Asupra unui vetor analog vectorului lui Galerkin pentru erhilibrul corporilor elastice ar isotropie tranversa. Bull. Stint., Ser. Mat. Fiz., Acad. Repub. Pop. Romane, 2, 207. [4] Moisil, A., 1951. Les relation entre les tensions pour les corps élastiques a isotropic transverse, Acad. Repub. Pop. Romane, Bul. Sw. Sect. Sti. Mat. Fiz., 3, 473480. [5] Nowacki, W., 1953. The Determining of Stresses and Deformations in Transversely Isotropic Elastic Bodies. Arch. Mech. Stos., 5, 545—556. [6] Hu, Hai-Chang, 1953. On the Three Dimensional Problems of the Theory of Elasticity of a Transversely Isotropic Body. Acta Physica Sinica, 9, 130—144 (in Chinese with English summary). [7] Hu, Hai-Chang, 1953. On the Three Dimensional Problems of the Theory of Elasticity of a Transversely Isotropic Body. Acta Scientia Sinica, 2, 145—151. [8] Hu, Hai-Chang, 1954. On the General Theory of Elasticity for a Spherically

Isotropic Medium. Acta Physica Sinica, 10, 57—69 (in Chinese with English summary).