Scientia Sinica

2 SCIENTIA SINICA

‘Vol, V where Aj, An 5° Age, %, % are constants, and Ay, — Ayn = 2 Age - (2) The equations. of motion are Oox OGry OT xz Ou XG = eo ert ey TheGe) cL COP? Ofey, Ody OT yz O2u Ci yp Ox os oy a Oz F p Oz? ” . (3) OTee aL OT yz fk, Oo: a Le = O*w

Ox ay | Oz PB i

where X, Y, and Z are the components of body forces and p is the specific mass of the body. Substituting expressions (1) into equations (3), we obtain equations of motion expressed in terms of displacement as follows:

O7u O7u O7u 62u Bi aa + Bes aye + Bu ee + PU aray ©

Orw oT O*u 1D eee Cr ae Ox we Or? Ou O7u 07u 620 Ve == By, = + By Ox Oy + Bes Ox? al 11 Oy? Brg Oz? alm Orn OT , Ow ohare eee ime a ? (4) Oru 670 O?w O2w Bis aoe + Fis 5 oz + By, Ox? + By, Oy? ats Orw or Oe + Ba Oz? +2 = 4; Oz eae Or? * | where By = Ai; B33 = A335 Bug = Ay; Bes = Age» (5) (S) By = Az + A 66» By3 = Ay3 + Ags i and By = By + Bee - (6)

In the following we shall simplify the fundamental system (4) by introducing suitable stress functions.