he temperature distnbution on the surface of a flight vehicle and the va-riation of the modulus of elasticity with respect to temperature are considered. The minimum weight structural design with constraints on freque...he temperature distnbution on the surface of a flight vehicle and the va-riation of the modulus of elasticity with respect to temperature are considered. The minimum weight structural design with constraints on frequency, on the coordinates ofmodal nodes and on the upper and lower bounds of the design vanables are studied us-ing Kuhn-Tucker conditions as optimal cntenon. The vanation of the flrst three ordernatural frequencies, modal shapes and minimum structural weight vs temperature gra-dient are discussed. It is pointed out that it is imperative to take into account the effectof aerodynamic heating on structural dynamic optimization. Calculation example showsthat the method obtained is feasible and efficient.展开更多
A set of universal equations on the reduced stress relaxation modulus with K-W-W stretched exponential function has been derived from the dynamics of α and β structural relaxation processes. In the present work, the...A set of universal equations on the reduced stress relaxation modulus with K-W-W stretched exponential function has been derived from the dynamics of α and β structural relaxation processes. In the present work, the K-W-W decay function is used to define the three types of relaxations (single α, single β relaxation and α-β co-relaxation), then their average times of relaxation are theoretically calculated from the reduced shear stress relaxation modulus and the relaxation time spectrum function H(τ). When the average time of co-relaxation, the reference temperatures (ficitive Tf and glass transition Tg) and the isostructural parameter achieved from the conditions of isostructural glass state are introduced into the reduced shear stress relaxation modulus (GT) under the equilibrium state, a set of correlations between isochoric fragility index (mvα, mvβ and mvαβ) and the coupling strength (α and β) under the reference temperatures are derived from the exact definition of isochoric fragility. So the theory of dynamic fragility for glass substances at isochoric state is developed. The theory can predict the following main features of structural relaxations and behavior of isochoric fragility: the temperature dependence of peak relaxation frequency exhibits a bifurcation with a pair of single α and single β relaxations; the temperature dependence of Stickel equation on 1/T exhibits two crossovers with VFTH(1) and VFTH(2) at the temperatures of Tf and Tg regime; there are two linear correlations between isochoric fragility index (mvα and mvβ) and the coupling strength. Fine agreements between the theoretical calculation and experimental results are obtained.展开更多
文摘he temperature distnbution on the surface of a flight vehicle and the va-riation of the modulus of elasticity with respect to temperature are considered. The minimum weight structural design with constraints on frequency, on the coordinates ofmodal nodes and on the upper and lower bounds of the design vanables are studied us-ing Kuhn-Tucker conditions as optimal cntenon. The vanation of the flrst three ordernatural frequencies, modal shapes and minimum structural weight vs temperature gra-dient are discussed. It is pointed out that it is imperative to take into account the effectof aerodynamic heating on structural dynamic optimization. Calculation example showsthat the method obtained is feasible and efficient.
基金supported by the National Natural Science Foundation of China (Grant No. 50973007)
文摘A set of universal equations on the reduced stress relaxation modulus with K-W-W stretched exponential function has been derived from the dynamics of α and β structural relaxation processes. In the present work, the K-W-W decay function is used to define the three types of relaxations (single α, single β relaxation and α-β co-relaxation), then their average times of relaxation are theoretically calculated from the reduced shear stress relaxation modulus and the relaxation time spectrum function H(τ). When the average time of co-relaxation, the reference temperatures (ficitive Tf and glass transition Tg) and the isostructural parameter achieved from the conditions of isostructural glass state are introduced into the reduced shear stress relaxation modulus (GT) under the equilibrium state, a set of correlations between isochoric fragility index (mvα, mvβ and mvαβ) and the coupling strength (α and β) under the reference temperatures are derived from the exact definition of isochoric fragility. So the theory of dynamic fragility for glass substances at isochoric state is developed. The theory can predict the following main features of structural relaxations and behavior of isochoric fragility: the temperature dependence of peak relaxation frequency exhibits a bifurcation with a pair of single α and single β relaxations; the temperature dependence of Stickel equation on 1/T exhibits two crossovers with VFTH(1) and VFTH(2) at the temperatures of Tf and Tg regime; there are two linear correlations between isochoric fragility index (mvα and mvβ) and the coupling strength. Fine agreements between the theoretical calculation and experimental results are obtained.
