Asymptotic and Spectral Analysis of the Bending-Torsion Vibration Model with Nondissipative Boundary Conditions
Date of Award
Program or Major
Doctor of Philosophy
Marianna A Shubov
John F Gibson
This dissertation is concerned with mathematical results on the initial boundary-value problem for the coupled bending-torsion vibration model, which is important in different areas of engineering sciences (e.g. design of bridges and tall buildings, aerospace engineering, etc.). Mathematically, the model is given by a system of two hyperbolic partial differential equations equipped with a 3-parameter family of nonselfadjoint (linear feedback type) boundary conditions. The system is represented as a first-order-in-time evolution equation in state space, a Hilbert space of 4-component Cauchy-data. It is shown that the dynamics generator is a nonselfadjoint matrix differential operator with a compact resolvent. The spectral equation of the generator is formulated using the method of reflection matrices. Precise asymptotic formulas are derived for the eigenvalues, which correspond to vibrational frequencies of the physical system.
Kindrat, Laszlo Peter, "Asymptotic and Spectral Analysis of the Bending-Torsion Vibration Model with
Nondissipative Boundary Conditions" (2019). Doctoral Dissertations. 2452.