Size effect and dynamic properties of 2D lattice materials

The dynamic analysis of two-dimensional (2D) periodic material structures is proposed via a novel mechanical approach. General assumptions include: i) the representative unit cell of the square lattice can be modeled by means of a defined number of straight micro-beams; ii) both shear/flexural and axial strains are locally accounted for; iii) a microstructure-dependent scale length is introduced as an intrinsic parameter of the micro-beams, with possible different scale lengths for different considered beams. All these features allow to detect the influence of the characteristics of the lattice at the local scale on the global dynamic behavior. Moreover, the existence of frequency band gaps is also predicted.