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Based on the variational theory,a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects.The supercell technique is applied.By expanding the displacement field and the material constants (mass density and elastic stiffness) in periodic wavelets,the explicit formula- tions of an eigenvalue problem for the plane harmonic bulk waves in such a phononic structure are derived.The point and line defect states in solid-liquid and solid-solid systems are calcu- lated.Comparisons of the present results with those measured experimentally or those from the plane wave expansion method show that the present method can yield accurate results with faster convergence and less computing time.
Based on the variational theory, a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects. The supercell technique is applied. By expanding the displacement field and the material constants ( mass density and elastic stiffness) in periodic wavelets, the explicit formula- tions of an eigenvalue problem for the plane harmonic bulk waves in such a phononic structure are derived. point and line defect states in solid-liquid and solid-solid systems are calcu - lated. Comparisons of the present results with those measured experimentally or those from the plane wave expansion method show that the present method can yield accurate results with faster convergence and less computing time.