Characterization of Vibrating Plates by Bi-Laplacian Eigenvalue Problems

Details Characterization of Vibrating Plates by Bi-Laplacian Eigenvalue Problems Characterization of Vibrating Plates by Bi-Laplacian Eigenvalue Problems

2008-06-05

arxiv.org/abs/0806.0879v2

Mathematics

Analysis of PDEs

The paper has been withdrawn by the author due to the improper submission

Scientific paper

In this paper we derive boundary integral identities for the bi-Laplacian eigenvalue problems under Dirichlet, Navier and simply-supported boundary conditions. By using these identities, we first obtain the uniqueness criteria for the solutions of the bi-Laplacian eigenvalue problems, and then prove that each eigenvalue of the problem with simply-supported boundary condition increases strictly with Poisson's ratio, thereby showing that each natural frequency of a simply-supported vibrating plate increases strictly with Poisson's ratio. In addition, we obtain boundary integral representations for the strain energies of the vibrating plates under the three boundary conditions.

Affiliated with

Also associated with

No associations

Rating

Characterization of Vibrating Plates by Bi-Laplacian Eigenvalue Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Characterization of Vibrating Plates by Bi-Laplacian Eigenvalue Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characterization of Vibrating Plates by Bi-Laplacian Eigenvalue Problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-127542