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In this paper, a type of new fractional order hyperchaotic Lorenz system is proposed. Based on the fractional calculus predictor-corrector algorithm, the fractional order hyperchaotic Lorenz system is investigated numerically, and the simulation results show that the lowest orders for hyperchaos in hyperchaotic Lorenz system is 3.884. According to the stability theory of fractional order system, an improved state-observer is designed, and the response system of generalized synchronization is obtained analytically, whose feasibility is proved theoretically. The synchronization method is adopted to realize the generalized synchronization of 3.884-order hyperchaotic Lorenz system, and the numerical simulation results verify the effectiveness.

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In this paper, a shear stiffness model for corrugated-core sandwich structures is proposed. The bonding area is discussed independently. The core is thought to be hinged on the skins with torsional stiffness. The analytical model was verified by FEM solution. Compared with the previous studies, the new model can predict the valley point of the shear stiffness at which the relationship between the shear stiffness and the angle of the core changes from negative correlation to positive correlation. The valley point increases when the core becomes stronger. For the structure with a angle of the core smaller than counterpart for the valley point, the existing analytical formulations may significantly underestimate the shear stiffness of the structure with strong skins. The results obtained by some previous models may be only 10 persent of that of the present model, which is supported by the FEM model.

The graded lattice structures have advantages in optimizing structure. In this paper, a parametric modeling method of graded lattice structure is proposed. The continuum damage model is used to evaluate the failure load of the structures. In this paper, two types of graded lattice structure are built by parametric modeling method: the cell-size-changed graded lattice structure (the densities of the structures are constant) and the bar-width-changed graded lattice structure (the masses of the structures are constant). The failure loads of the structures under three-point bending load are investigated. The results show that the smaller middle cell improves the bending failure load of the cell-size-changed graded lattice structures up to 52%, and the wider sandwich bar in the middle of the structure improves the bending failure load of the Bar-width-changed graded lattice structures up to 31%. Meanwhile, the graded parameter of the structures will influence the failure mode of the structures.