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Full-Text Articles in Physical Sciences and Mathematics
Robust Sensor Design For The Novel Reduced Models Of The Mead-Marcus Sandwich Beam Equation, Ahmet Aydin
Robust Sensor Design For The Novel Reduced Models Of The Mead-Marcus Sandwich Beam Equation, Ahmet Aydin
Masters Theses & Specialist Projects
Novel space-discretized Finite Differences-based model reductions are proposed for the partial differential equations (PDE) model of a multi-layer Mead-Marcus-type beam with (i) hinged-hinged and (ii) clamped-free boundary conditions. The PDE model describes transverse vibrations for a sandwich beam whose alternating outer elastic layers constrain viscoelastic core layers, which allow transverse shear. The major goal of this project is to design a single boundary sensor, placed at the tip of the beam, to control the overall dynamics on the beam.
For (i), it is first shown that the PDE model is exactly observable by the so-called nonharmonic Fourier series approach. However, …
Analysis Of Boundary Observability Of Strongly Coupled One-Dimensional Wave Equations With Mixed Boundary Conditions, Wilson Dennis Horner
Analysis Of Boundary Observability Of Strongly Coupled One-Dimensional Wave Equations With Mixed Boundary Conditions, Wilson Dennis Horner
Masters Theses & Specialist Projects
*see note below
In control theory, the time it takes to receive a signal after it is sent is referred to as the observation time. For certain types of materials, the observation time to receive a wave signal differs depending on a variety of factors, such as material density, flexibility, speed of the wave propagation, etc. Suppose we have a strongly coupled system of two wave equations describing the longitudinal vibrations on a piezoelectric beam of length L. These two wave equations have non-identical wave propagation speeds c1 and c2. First, we prove the exact observability inequality with the optimal …