T gj sj

QUASITANGENTIAL VIBRATIONS

These vibrations are characterized by the relations iii » vv, 0 < s < 1.

The principal problem asymplotics for quasitangential vibrations can be obtained by putting a = 2s, b - 0, and r = —s in formulas 23.9. The principal error is a quantity of order e, where e = 0{ ifs).

The equations of quasitangential vibrations coincide with those of the plane problem and have the form

A i dai A2da2

The principal problem system 23.19 is integrated, taking into account the tangential conditions. The auxiliary problem equation consists of integrating 20.8 to 20.13 where we put

S 4h2B

The stressed state, described by the auxiliary problem, is oscillating. Its variability in the direction normal to the edge is (1 ¡2 + s/2) and exceeds the variability of the simple edge effect, which is 1/2.

RAYLEIGH-TYPE VIBRATIONS WITH 0 < s <1/2

These vibrations are realized in a shell whose edges are fixed in such a way that its middle surface can bend, say, when all the edges of the shell are free. The principal problem system of equations is an analogue of the dynamic equations of the pure moment state described in Section 11. This system looks like

— + — +---— + — -— + kiNi + k\N-> + 2hpu> w = 0

1 dGj 1 dHu

A] dai a2 acv2

0 0