Dynamic and buckling analysis of a thin elastic-plastic square plate inca uniform temperature field

The nonlinear models of the elastic and elastic-linear strain-hardening square plates with four immovably simply-supported edges are established by employing Hamiltons Variational Principle in a uniform temperature field. The unilateral equilibrium equations satisfied by the plastically buckled equilibria are also established. Dynamics and stability of the elastic and plastic plates are investigated analytically and the buckled equilibria are investigated by employing Galerkin-Ritzs method. The vibration frequencies, the first critical temperature differences of instability or buckling, the elastically buckled equilibria and the extremes depending on the final loading temperature difference of the plastically buckled equillibria of the plate are obtained. The results indicate that the critical buckling value of the plastic plate is lower than its critical instability value and the critical value of its buckled equilibria turning back to the trivial equilibrium are higher than the value. However, three critical values of the elastic plate are equal. The unidirectional snap-through may occur both at the stress-strain boundary of elasticity and plasticity and at the initial stage of unloading of the plastic plate.

COHERENT STRUCTURES IN COUNTERCURRNET AXISYMMETRIC SHEAR FLOWS

The dynamical behaviors of coherent structures in countercurrent axisymmetric shear flows are experimentally studied.The forward velocity U1 and the velocity ratio R=(U1-U2)/(U1+U2),where U2 denotes the suction velocity,are consldered as the control parameters.Two kinds of vortex structures,i.e.,axisymmetric and helical structures,were discovered with respect to different reginmes in the R versus U1 diagram .In the case of U1 rangjing from 3 to 20m/s and R from 1 to 3,the axisymmetric structures plan an important role.Based on the dynamical behaviors of axisymmetric structures,a critical forward velocity U1cr=6.8m/s was defined,subsequently,the subcritical velocity regime:U1>U1cr and the supercritical velocity regime:U1<U1er,In the subcritical velocity regine,the flow system contains shear layer self-excited oscillations in a certain range of the velocity ratio with respect to any forward velocity.In the supercritical velocity regime,the effect of the velocity ratio could be explained by the relative movement and the spatial evolution of the axisymmetric structure undergoes the following stages:(1) Kelvin-Helmholtz instability leading to vortex rolling up,(2) first time vortex agglomeration.(3) jet colunn self-excited oscillation,(4) shear layer self-excited oscillation,(5)"ordered tearing",(6) turbulence in the case of U1<4m/s (the "ordered tearing" does not exist when U1>4m/s),correspondingly,the spatial evolution of the temporal asymptotic behavior of a dynamical system can be described as follows:(1) Hopt bifurcation,(5) chaos("weak turbulence")in the case of U1<4m/s(superharmonic bifurcation does not exist when U1>4m/s).The proposed new terms,superharmonic and reversed superbarmonic bifurcations,are characterized of the frequency doubling rather than the period doubling.A kind of unfamiliar vortices referred to as the helical structure was discovered experimentally when the forward velocity around 2m/s and the velocity range from 1.1 to 2.3,There are two base frequencies contained in the flow system and they could coexist as indicated by the Wigner-Ville-Distribution and the temporal asymptotic behavior of the dynamical system corresponding to the helical vortex could be described as 2-torus as indicted by the 3D reconstructed phase trajectory and correlation dimension.The scenario of the spatial evolution of helical structures could be described as follows:the jet column is separated into two parts at a certain spatial location and they entangle each other to form the helical vortex until the occurrence of those separated jet columns to reconnect further downstream with the result that the flow system evolves into turbulence in a catastrophic form.Correspondingly,the dynamical system evolves directly into 2-tiorus through the supercritical Hopf bifurcation followed by a transition from a quasi-periodic attractor to a strange attractor.In the case of U1=2m/s,the parametric evolution of the temporal asymptotic behavior of the dynamical system as the velocity ratio increases from 1 to 3 could be described as follows:(1)2-torus(Hopf bifurcation),(2) limit cycle(reversed Hopf bifurcation),(3) strange attractor (subbarmonic bifurcation).