Flexural Wave Band Gaps in Periodic Bi-Directionally Orthogonal Stiffened Plates with Holes

Abstract

Plate frame structure with holes is a novel candidate to reduce the weight and strengthen the architectural structures to fulfill the requirements of practical engineering applications. The designed periodic hole structure can generate a band gap from the perspective of the frequency spectrum. In this study, a new band gap calculation method was proposed under the basic energy method framework for the analysis of hole periodic structures. Gaussian wavelet function with a good localization characteristic was adopted to overcome the inaccurately assumed displacement filed function due to the introduced hole issue. The entire plate structure was divided into cell elements and an artificial spring model was introduced to satisfy the cell coupling conditions. The coupling constraints were converted into elastic potential energy to be added to the energy functional for the entire system. The dispersion curves obtained by this method are in excellent agreement with the results of the finite element method. It was observed that periodic hole plates lead to the generation of complete and directional flexural wave band gaps. By introducing bi-directionally orthogonal stiffeners, the band gap of periodic hole plates could be significantly lengthened and complete band gaps could be successfully generated. Furthermore, geometrical parametric studies on flexural wave band gaps were analyzed. A wide and complete band gap could be realized by increasing the width of the stiffener to a certain extent, but not fully proportional.