Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Peter Torvik, PhD


In this dissertation, different aspects of constrained layer damping treatments on beams of various geometries are studied. First, the optimal length of a constrained layer damping treatment mounted on a surface in linear strain is identified as a function of the relative stiffnesses of the damping layers and the non-uniformity of the surface stain. The analysis extends previous work that considered the case of uniform surface strain. Sixth order sandwich beam theory is then modified for use with a rectangular beam covered with a segmented constrained layer damping treatment. Non-dimensional variables are used to simplify the form of the problem. Also, equations are developed for a beam of circular cross section with thin narrow constrained layer strips placed parallel to the beam centerline, and it is shown the equations have the same form as the sixth order theory for the rectangular beam. A new approximation method, the "Complex Rayleigh Quotient", is proposed to estimate the complex natural frequency and damping of structures. Complex mode shapes are used in a ratio similar in spirit to Rayleigh's Quotient to obtain an estimate for the complex frequency of the system. The method is defined for both discrete and continuous systems, and illustrated using a rectangular beam with a segmented damping treatment. The estimates of loss factor developed from the Complex Rayleigh Quotient were much closer to the exact solutions than those developed using the Modal Strain Energy method. A new constrained layer configuration, the" barberpole", is presented for beams of circular cross section. An analysis is developed which show that the barberpole configuration can damp both bending and torsional vibrations. The barberpole also provides more damping than unsegmented strips for a beam in bending. An experiment was performed to gain confidence in the bending portion of the barberpole analysis.

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The author's Vita page is omitted.