In this paper we consider the stability of viscoelastic plates in shear. The problem is solved by theory of pseudo-bifurcation points and "elastic analogy" method [2] in two cases: isotropic viscoelastic and orthotropic viscoelastic plates. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 2 {46- 54) STABILITY OF VISCOELASTIC PLATES IN SHEAR PRAM QUOC DOANH, TO VAN TAN Hanoi University of Cim'l Eng:'neering 1. Introduction In [1] the stability of viscoelastic plates in compression is investigated In this paper we consider the stability of viscoelastic plates in shear. The problem is solved by theory of pseudo-bifurcation points and "elastic analogy" method [2] in two cases: isotropic viscoelastic and orthotropic viscoelastic plates. 2. Stability of viscoelastic isotropic plates in shear A. Elastic stability of plates in shear Let us consider elastic stability of plates (ax b) with simply supported edges. From [3] we have the elastic stability equation of plates in shear as follows: - t ~ - - l rr a I ~ -~ X b l z- y () where N xy {j : = r xy · fi : shearing force thickness of plates : "stimulus" displacement. 46 Modulus D= Eo 3 12(1 - 11 2 ) Go 3 - () 6(1 - 11) a/ b: The critical stress of elastic plates depends on the rate 1r2 02 Tcr = K b28 = K6b2(1- 11). G 11"2 D ajb K () 00 B. Viscoelastic stability of plates in shear Let us consider the equation of state [4]: 1(t) = ~w) - t 2[1 + 11(t)] j T(tl)K(t, tl)dt () 1 0 where: T(t), 1(t) -shearing stress and shearing strain and Gt E(t) ()- 2[1+ 11(t)] It can be assumed that E(t) const, from () we get : = E = canst, G= () G(t) = G = canst, 11(t) = 11 E 2(1 + 11) = () We denote lo(t), To(t) - strain and stress in basic state, 1(t), T(t) - in the adjacent state such that ~T = T- To~ To, ~~ =1 -Ia ~ ~T, ~~ Ia, -called "stimulus". Equation () can be written for ~T, ~~in the form: ~1(t) = ~~t) t - 2(1 + 11) j M(tr)K(t, tr)dtr. 0 47 With the help of () we have: !:!"( = t ~ [ - E f () M(t!)K(t, t 1 )dt 1 .
