Polyimidines. VI. The comparison of polyimidines from bis(3,3-diphenyl-6-phthalidyl) ketone

New thermally stable polyimidines have been synthesized from bis(3,3-diphenyl-6-phthalidyl) ketone and five diamines: o-phenylenediamine, m-phenylenediamine, 1,5-diaminonapthalene, 1,8-diaminonapthalene, and benzidine. Polymers of low molecular weight (inherent viscosity up to 0.24 dl/g) were obtained by solution and sealed-tube polymerizations. The structural differences of the amines provided information concerning the effects on the thermal stability properties of the resulting polyimidines. The yellow to black polymers exhibited a 10% loss ranging from 420–510°C in air and 460–555°C in nitrogen and were soluble in chloroform and dimethylformamide.     

NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.     

A second-order dynamic subgrid-scale stress model

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎＬＥＳ,ｔｈｅｌａｒｇｅｓｃａｌｅｓｉｎｔｈｅｆｌｏｗａｒｅｃｏｍｐｕｔｅｄｅｘｐｌｉｃｉｔｌｙａｎｄｔｈｅｓｕｂｇｒｉｄ＿ｓｃａｌｅｓ(ＳＧＳ),ｗｈｉｃｈａｒｅｆｉｌｔｅｒｅｄｏｕｔｂｙａｎａｖｅｒａｇｅｐｒｏｃｅｓｓｏｐｅｒａｔｉｏｎｏｎｔｈｅＮａｖｉｅｒ＿Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓ,ａｒｅｍｏｄｅｌｅｄ.ＳｉｎｃｅＬＥＳｒｅｑｕｉｒｅｓｌｅｓｓｃｏｍｐｕｔｅｒｔｉｍｅｔｈａｎｔｈｅｄｉｒｅｃｔｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓａｎｄｕｓｅｓｓｉｍｐｌｅｒａ…     

Thermoelastic free vibration of clampe circular plate

An analysis was given for the free vibration of clamped circular plate when temperature and stress fields were coupled. A nonlinear differential equation about time was obtained by using Galerkin’s method. The numerical results of vibration amplitude vs time were compared with the uncoupled case. It is found that if the given initial displacement is small, the effect of thermoelastical coupling will make the natural frequency increase; if the given initial displacement is large, it will be the opposite case. Effects of some different vibration factors are also discussed.     

SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR (Ⅰ)—FUNDAMENTAL BEHAVIOR

The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elasto~plasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concept of `cohesive crack’ was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.     

An analytic and application to state space reconstruction about chaotic time series

The state space reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: N.H.Packard, F.Takens, M. Casdagli, J.F.Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time τ were identified. The influence for state space reconstruction of lag time τ was discussed. The result tells us that is a good practical method for state space reconstruction.     

Equivalent Boundary Integral Equations with indirect unknowns for thin elastic plate bending theory

Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE. Paper from SUN Huan-chun, Member of Editorial Commitee, AMM Biography: ZHANG Yao-ming (1962-)