Design of band-gap grid structures

This paper discusses issues related to designing band-gaps in periodic plane grid structures. Finite element analysis is used to solve the dynamic behavior of a representative unit cell and Bloch-Floquet theory is used to extend the results to the infinite structure. Particular attention is given to the addition of non-structural masses that are introduced as design variables. These are used to create desirable features in the dispersion diagram. Physical insight is presented into the optimal choice of locations where masses should be added and the results of several numerical examples are provided to highlight this and other features of how band-gaps can be created and located at desired frequency ranges. The effect of the skew angle of the underlying grid structure is also explored, as are mathematical refinements of the modelling of the beam elements and the rotational inertia of the added masses. A scaling feature between the size of the reducible and the irreducible reference cell is exploited and the manner in which this can simplify optimization approaches is discussed.