| Summary: | 碩士 === 國立成功大學 === 機械工程學系 === 107 === First, this research discusses dynamically effective properties of metamaterials. A single resonance model, i.e., periodic spring mass system with sub-structure , was proposed.
Based on the dynamically effective properties method proposed from Liu et al. [8] and Oh et al. [10], the dynamically effective mass and elastic property of the model are derived and found to be frequency dependent. With Oh et al.’s [10] method, the model is equivalent to a single mass spring system, and the dispersion relation of the model could be obtained. Then the dynamically effective material properties of the equivalent system could be calculated by Liu et al.’s [8] method. Corresponding to the model dispersion curve to see whether the band gap always coincides with the frequency range of negative effective properties, the correctness of dynamically effective properties method proposed from this research was verified.
Second, a spatio-temporal metamaterial model was proposed to demonstrate nonreciprocal wave propagation for elastic wave. Nonreciprocal wave propagation means the transmission of energy in opposite directions between any two points in space will have asymmetric wave propagation information. The dispersion relation of the model could be theoretically calculated using lattice dynamics. In order to improve the complexity of the theoretical derivation processes, a numerical simulation combining finite difference time-domain method and perturbation method was proposed. With numerical perturbation method, the model dispersion curve could be quickly and numerically calculated. The wave propagation behavior inside the model was simulated using finite difference method and the nonreciprocal wave propagation of the elastic waves were further illustrated.
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