| I employ the adjacent-equilibrium-position method (static stability method) to assess stability of two novel systems that exhibit greatly-enhanced damping: a structural component consisting of flat-ended columns compressed by flat unattached platens; and a solid composite consisting of a negative-stiffness cylinder with a positive-stiffness coating. In Chapter 1, buckling of compressed flat-end columns loaded by unattached flat platens is analyzed. I show theoretically that buckling occurs first at the critical load and associated mode shape of a column with built-in ends, followed extremely closely by a second critical load and different mode shape characterized by column end-tilt. The theoretical critical load for secondary or end tilt buckling is shown to be only 0.13% greater than the critical load for primary buckling for the column geometries examined, in which the ends are in full contact with the compression platens. These results agree well with experiments performed by UW colleagues. In Chapters 2 and 3, I first show how to analyze the stability of a solid composite consisting of a negative-stiffness cylinder with a positive-stiffness coating, previously analyzed dynamically, by the comprehensive but simpler static stability approach. I then employ this approach to show that permitting heterogeneity of the positive-stiffness phase can substantially increase the range of constituent negative stiffness while maintaining overall composite stability. In Chapter 2, I treat the positive-stiffness phase heterogeneity as piecewise homogeneous, while in Chapter 3 I treat it as continuously-varying. In both cases, I determine the heterogeneity type that permits the greatest range of constituent negative stiffness while maintaining overall composite stability. In Chapter 4, I expand results obtained for elastic composite solids to viscoelastic ones in which both phases are comprised of linear, isotropic, viscoelastic materials by employing the correspondence principle. I demonstrate that the specific heterogeneity of the positive-stiffness phase that was shown in Chapter 3 to permit the largest inclusion negative stiffness while maintaining overall composite stability, can increase the effective loss tangent of the composites near the stability boundary and decrease the critical exciting frequency at which the dynamic effective composite bulk modulus becomes infinite. |
