Abstract
Wave-based higher-order rod models are formulated to calculate Bragg scattering band gaps and forced responses of periodic structures and phononic crystal using the Spectral Transfer Matrix (STM) and the Wave Finite Element (WFE) methods. STM is a wave propagation spectral method based on the transformation of a coupled second-order ordinary differential equation (ODE) in a system of first-order by using the state-space formulation. WFE is a wave-based finite element approach developed to calculate dynamic behavior in periodic acoustic and structural systems. Three higher-order rod theories, Love (one-wave mode), Mindlin-Herrmann (two-wave modes), and Mindlin-McNiven (three-wave modes) are formulated by STM and WFE methods. Applying the Bloch-Floquet theorem to periodic rod structures, dispersion diagrams, and forced responses are obtained from Bragg wavenumbers and wave modes. In order to evaluate the performance and efficiency of the wave-based higher-order rod models, numerical examples are simulated and the results are verified. An experimental test is performed for an actual PC rod and the results are used to validate the numerical ones.
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