偏微分方程式セミナー: Asymptotic behavior of eigenfrequencies of a thin elastic rod with non-uniform cross-section, Albert Rodriguez Mulet 氏

開催日時

2018年6月8日 16時30分 ～ 2018年6月8日 17時30分

場所

北海道大学理学部3号館3-309室

講演者

Albert Rodriguez Mulet 氏 (北海道大学)

We study the eigenvalue problem of the second order elliptic operator which arises in the linearized model of the periodic oscillations of a homogeneous and isotropic elastic body. The square of the frequency agrees to the eigenvalue. Therefore, analyzing the properties of the eigenvalue we can retrieve information on the frequency of the oscillations. Particularly, we deal with a thin rod with non-uniform connected cross-section in several cases of boundary conditions. We see that there appear many small eigenvalues corresponding to the bending mode of vibrations of the thin body. We investigate the asymptotic behavior of these eigenvalues and obtain a characterization formula of the limit equation when the thinness parameter tends to 0.