DE Seminar: Ahmet Kaan Aydin (UMBC)

Abstract: Space-discretized Finite Difference approximations for the multi-layer Mead-Marcus beam model (PDE) with both hinged and cantilevered boundary conditions are investigated. The PDE model itself describes transverse vibrations for a multi-layer sandwich beam whose outer layers are piezoelectric or elastic, and the constrained layers are viscoelastic. Even though the PDE model (with either type of boundary conditions) is known to be exactly observable with a single observation on its boundary, the discretized models are not able to retain the exact observability uniformly with respect to the mesh parameter. This is mainly due to the loss of the uniform gap among the eigenvalues as the mesh parameter goes to zero. Two techniques are implemented: Direct Fourier Filtering and Order-Reduction. It is shown that the uniform observability is recovered uniformly with respect to the mesh parameter. Recent results and open problems will be discussed, and the Wolfram Demonstrations Projects will be shared with the audience.