Date of Award

Spring 2019

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Marianna A Shubov

Second Advisor

Mark Lyon

Third Advisor

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.

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