PDE Seminar (2019/6/28): Asymptotic analysis of stretching ang torsional vibrations of thin axissymmetric elastic rods
 Date

2019628 16:30 
2019628 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 lowfrequency eigenvalues corresponding to the bending mode of vibrations. We see as well that there appear midfrequency eigenvalues corresponding to torsional and stretching modes of vibrations. We investigate the asymptotic behavior of these midfrequency 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.