Two-dimensional periodic structures modeling based on second strain gradient elasticity for a beam grid

Higher order gradient elasticity theories are widely applied to determine the wave propagation characteristics of micro-sized structures. The novelty this paper, firstly, is using Second Strain Gradient (SSG) theory explore mechanism a 2D beam grid. strong formulas continuum model including governing equations and boundary conditions derived by Hamilton principle. Then, valuable long-range Lattice Spring Model (LSM) elaborated, providing reasonable explanation for based on SSG theory. dynamic from LSM calculated through Fourier series transform approach. Finally, properties grid analyzed within Wave Finite Element Method (WFEM) framework. band structure slowness surfaces, confined irreducible first Brillouin zone, studied in frequency spectrum. energy flow vector fields beaming effects discussed Classical Theory (CT) elasticity. results show that proposed approach significant potential investigating complex periodic