In this paper, a novel three-dimensional (3D) lattice honeycomb is developed based on a two-dimensional (2D) accordion-like honeycomb. A combination of theoretical and numerical analysis is carried out to gain a deeper understanding of the elastic behavior of the new honeycomb and its dependence on the geometric parameters. The results show that the proposed new honeycomb can simultaneously achieve an in-plane negative Poisson’s ratio (NPR) effect and an out-of-plane zero Poisson’s ratio (ZPR) effect. This unique property may be very promising in some important fields, like aerospace, piezoelectric sensors and biomedicine engineering. The results also show that the geometric parameters, such as the slant angle, the strut thickness and the relative density, have a significant effect on the mechanical properties. Additionally, different dominant deformation models of the new honeycomb when compressed along the x (or y) and z directions are identified. This work provides a new concept for the design of honeycombs with a doubly unusual performance.
In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details.
This paper presents a high order symplectic conservative perturbation method for linear time-varying Hamiltonian system. Firstly, the dynamic equation of Hamiltonian system is gradually changed into a high order perturbation equation, which is solved approximately by resolving the Hamiltonian coefficient matrix into a "major component" and a "high order small quantity" and using perturbation transformation technique, then the solution to the original equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a symplectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, efficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation order, the perturbation solutions tend to exact solutions rapidly.
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