Effective dynamic properties of multi-segment beam lattices: a dynamic stiffness formulation

We examine the macroscopic moduli of lattices composed of multi-segment beams (MSBs), each of which includes more than one segment with independent geometric and material parameters, with a belief that a wider adjustable range can be obtained via introducing such MSB. To investigate the frequency dependence of effective moduli, we propose a dynamic stiffness formulation which is exactly calculated based on corresponding equations of motion. First, the MSB is taken as a multi-node finite element and its stiffness matrix is derived with the help of continuity requirements on inner joints. Then, macroscopic properties are obtained one by one by force analysis on the structural unit cell subjected to various external macrostress fields, resulting in exact analytical frequency-dependent expressions of effective moduli. The above formulation is verified by comparing with the dynamic finite element method (DFEM), and it shows the predicting ability in high-frequency domain. Compared to lattice with one-segment homogeneous truss, effects of geometric and material parameters of the truss segments on the macroscopic properties are investigated systematically. The adoption of MSBs is believed to be a feasible way of adjusting effective properties of lattices.