PDE Seminar (2019/6/28): Asymptotic analysis of stretching ang torsional vibrations of thin axis-symmetric elastic rods

Date
2019-6-28 16:30 - 2019-6-28 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 axial symmetry and clamped ends. It is known that there are many low-frequency eigenvalues corresponding to the bending mode of vibrations. We see as well that there appear mid-frequency eigenvalues corresponding to torsional and stretching modes of vibrations. We investigate the asymptotic behavior of these mid-frequency eigenvalues, we obtain a characterization formula of the limit equation when the thinness parameter tends to 0 and we give a result on the strong convergence of the corresponding eigenfunctions.