Scientia Sinica

. No. 1 HU; EQUILIBRIUM © VIBRATION OF TRANSVERSELY ISOTROPIC ELASTIC BODY 15

Let Fi and F2 be the solutions of the equations

— . F; : ViFit a a G52) (81) Tt is evident that P= Fy ots . (82)

is a solution of equation (80). Substituting (82) into (71), and putting

OF, OF; —— ——— = a5 = > 8 at : P1> ac P25 P Po ( 2)

we finally obtain the following expressions:

_ OP: _ OP, OPo ay ay + ae? (84) a—s? (y—k c?) OP; w=—> = ee

7=1,2

It is clear that ~; and @, satisfy the same equations as Fi and FP.

The propagation of axisymmetric waves in transversely isotropic circular cylinder has been investigated by C. Chree™*! and R. W. Morse!”!,

VIII. Vzisrations oF Boptes oF REVOLUTION

Consider a transversely isotropic elastic body of revolution with planes of isotropy perpendicular to the axis of revolution. Take as cylindrical coordinates r, 8, and z, such that the z-axis coinsides with the axis of revolution. In cylindrical coordinates we have the following formulas:

oe, EEE OPE " @rdz or OB” on, ae OF OP co r SOlon Or ° (85) o7F OF w=aVviF+y Oz? en Cerra

The stress functions F and ¢@ satisfy equations (72) and (73) respectively, in which the differential operator V? takes the form