Synthesis of phononic periodic structures with dynamic damping structure

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The present study intended to develop a numerical methodology that can be utilized for synthesizing the periodic structures shutting out the vibration. Such a structure might be realized by embedding substructures, which work as dynamic dampers, comprising different material properties from that of the matrix material. In the present research, we have to repeat calculating the wave transmission properties of infinite and/or finite periodic structures. Moreover, we have to optimize the shape and topology of the periodic structures by repeating the transmission and eigenfrequency analyses. Thus, we developed a fundamental computation algorithm for twodimensional and three-dimensional problems using the boundary element method incorporated with the periodic boundary conditions. Because the final system matrix obtained by the boundary element method provides a nonlinear eigenvalue problem, standard eigensolver has not been used so far. In this study, we applied a contour integral method, so-called block SS-method, to solve this nonlinear eigenvalue problem.