An investigation of the stability of a linear viscoelastic bar

dc.contributor.committeeMemberChilds, S. Bart
dc.creatorFaust, Carl Dennis
dc.description.abstractThe intent of this study is to investigate the stability of an initially straight, simply supported, linear viscoelastic bar subjected to a harmonically varying axial load. Infinitesimal viscoelasticity is assumed through the study. The study is based upon the concepts of continuum mechanics developed by W. Noll. A Volterra integral of the second kind is derived and solved for the deflection of the bar as a function of time. The solution of the equation is based on the assumption that the stress relaxation function can be approximated as a series of monotonically decreasing exponentials. The study proceeds by defining the concept of the systems stability. Based on the general solution, two- lemmas and a theorem are proved with respect to stability. The theorem proves that two conditions are necessary and sufficient for stability. A numerical example is presented for which four cases are investigated. The stress relaxation function, c(t), is assumed to be a single exponential. The lemmas and theorem are applied to determine the system's stability.
dc.description.departmentMechanical Engineering, Department of
dc.format.digitalOriginreformatted digital
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleAn investigation of the stability of a linear viscoelastic bar
dc.type.genreThesis College of Engineering Engineering, Department of Engineering of Houston of Science


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