In–plane vibration analysis of plates with periodic skeletal truss micro–structures

The present contribution analyzes the dynamic in–plane behaviour of two–dimen- sional finite lattices consisting of periodic micro–skeletal truss structures made either by bar or beam elements. An homogenization asymptotic technique, employing the Fourier transform of the dynamic equilibrium equations of the discretized medium, is applied to derive the partial differential equations describing the in–plane vibration of an equivalent homogeneous plate. The resulting set of partial differential equations is then analyzed for deriving explicit relationships between reference–cell properties and homogenized continuum properties, i.e. parent material properties. Specific selection criteria are found for geometric and material parameters of the reference–cell in view of getting orthotropic as well as isotropic homogenized plates. Finally, the effects of micro–structural properties on the vibrating behaviour of the homogenized plate are investigated in terms of modal analysis, studying their influence on natural frequencies.