PDE Seminar (2018/6/8): Asymptotic behavior of eigenfrequencies of a thin elastic rod with non-uniform cross-section

Date
2018-6-8 16:30 - 2018-6-8 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Albert Rodriguez Mulet (Hokkaido University)
 
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.