Scientia Sinica

16 SCIENTIA SINICA Vol. V

1 oO oO 1 0 =— r

7 OM Vor 7 OG? ~ (86)

2 Wi

There are three important modes of vibration of bodies of revolution. Let us examine these modes individually.

1. Torsional vibration. In the case of torsional vibration, we may put

EA lfe P=P(r,2,t). (87) Consequently we obtain OP DOR D5 (88) 1 0 1 Op xc OD _ 7" + Or OF i sh Oz? Vasc Oca Ore (89)

Among the six stress components in cylindrical coordinate, four equal zero and the remaining two are related to @ by the relation

_ 3, OF = vp 1 o Tz = Da, are” Tro = Bee Or? aor ) 5 (90) For isotropic bodies, Bi, = Beg = # we have OP ee ee _ (#e 1 Op oO 6p? SE apoz? VO =e EG a G Only - ©) 1 0 © , OP ep OP _ r Or” Or | Oe pp OF " ©2) For transversely isotropic bodies, by substituting szZ—C,; 50 Tez = Tees (93) we have O 3? 3? 1 oO ug — —, Tot = Bes a ap > Tr6 = Be6e — ——s = y (94)

a oP ep OP _ r Or” Or * OC? Be Of” 2)

These two sets of equations are identical with (91) and (92). This fact indicates that the problem of torsional vibration of transversely isotropic bodies of revolution can be reduced to that of isotropic bodies of revolution.

2. Axtally symmetrical vibration. In the case of axially symmetrical vibration, we may put