WAVE PROPAGATION IN POLAR PERIODIC STRUCTURES USING FLOQUET THEORY AND FINITE ELEMENT ANALYSIS

In this paper, a generalised approximated approach to study wave propagation in structures that exhibit radial and/or circumferential periodicity is presented. Only a circular sector of the structure is studied, which could be a circumferential period or an arbitrary slice according to the kind of periodicity of the structure (radial, circumferential, both radial and circumferen-tial). The slice is then approximated using piecewise Cartesian waveguides, whose wave characteristics are obtained by the theory of wave propagation in periodic Cartesian structures and Finite Element analysis. Wave amplitudes change due to the changes in the geometry of the slice are accommodated in the model assuming that the energy flow through the interfaces of each Cartesian waveguide is the same. Results are validated considering the response of an infinite isotropic thin plate excited by a point harmonic force, showing the accuracy of themethod and the computational advantage compared to a standard FE harmonic analysis forinfinite structures. A numerical example of a polar periodic structure, mimicking a spider web, is also presented to investigate the potential applications of the method.