Scientia Sinica

No. 1 HU: EQUILIBRIUM « VIBRATION OF eee ISOTROPIC ELASTIC BODY 11

into equations (47), and then, integrating with respect to x, y, and z respectively, we obtain

oP Ay By age

= Ay Bi ae

Bys + 3 Bee ae s eel Ol, (54) coral oni gians

This system of ae can be satisfied by taking

oP 1 op 1 O27 = zt Sy eae can: eam oe Ay (s? By,—B1) + A3 s* B33 = say, (56)

— A, By3 + As (ss B33—By4) = s* a3.

Since T satisfies equation (52), the two equations of (55) have a common solution. Solving system (56), we get

Des st Lay (s? B33—By4) —@3 By3] By Byts? (BR—Bu B33—Baa) +s" B33 Bag *

(57) s* [ay By3+a3 (s? By,—By1) |

ia By By ts? (BRB B33—Ba) +s* B33 Bas ‘

VI. Stress FUNCTIONS FOR THE VIBRATION OF A [RANSVERSELY

Isotropic Exastic Bopy

Consider now the vibration of a transversely isotropic elastic body under surface tractions. For this problem the fundamental system (4) is reduced to the form

O7u O7u O7u Ow Oru

Bittman ax D Slee oti wmcre Oy 2 See Baa mere Oz w2' + Ba peg + Bi ope = 0 ge

we oa Ou O*u Ow O7u By Laas yt 8 al Ox => Bia sae ye ste Baal ames Oz? gi 2 isiarene mG oiz (58)

O*u O7u Ow Or w Orw Ow Bisaeor | 9! oy Oz + Bis Sr Se emer by? ca 33 oa Caan

We shall simplify this system of equations by the method proposed in paper [13]. As before, we first express # and v in terms of two stress functions F and @ as follows: