Modal properties of a cyclic symmetric hexagon lattice

Analyzed are the modal properties of a hexagon lattice formed of equilateral triangles. Cyclic symmetry is utilized to reduce the size of the problem to that of repeated segments. Four distinct sets of eigenvalues are determined for the independent symmetric components of the displacement vector along the two sides of a segment. In the physical domain, the dynamic stiffness matrix of the cyclic segment is determined analytically by solving for the state vectors from unit displacements independently applied at junction nodes. The cyclic model is validated with analytical results from the complete hexagon. The effect of curvature on modal properties is evaluated by comparing generalized quantities of flat and curved geometries.

► Cyclic symmetry transformation converts problem of large order to several of small order.
► Eigenvalues of dynamic stiffness matrix determined by iteration.
► Lattice yields modes from 2 groups; out-of-plane, & dense clusters of inplane.
► Curvature raises modal density, and couples in-plane and out-of-plane motions.