Equivalent in-plane dynamic elastic moduli of lattice structures with Plateau borders

Abstract

Lattice structures with Plateau borders (LSPB) have attracted increasing interests recently due to the improved stiffness, strength, energy absorption properties. Undoubtedly, vertexes with Plateau borders (VPB) play a significant role on the dynamic elastic moduli. This paper proposes an analytical framework of the frequency-dependent equivalent in-plane dynamic elastic moduli (Young’s moduli E1(ω), E2(ω), Poisson’s ratio ν12(ω), ν21(ω) and shear modulus G12(ω)) of LSPB. First, dynamic stiffness (DS) matrix of a lattice cell edge (based on rod and Timoshenko theories) connected to VPBs (modelled as rigid bodies) at both ends is formulated. Then, based on the above DS matrix and the unit cell method, closed-form expressions of equivalent in-plane dynamic elastic moduli are proposed, which are sufficient general to be applied to four types of lattices. The effects of mass, inertia moment and size of VPB on the equivalent dynamic elastic moduli are studied, with both physical and mathematical interpretations. Furthermore, the proposed expressions are applied to honeycomb, rectangular, auxetic and rhombus LSPB and some interesting and important observations are made. This research provides analytical expressions for broadband dynamic elastic moduli of LSPB, which can be directly used in the design and optimization of composite structures with lattice cores.