Stable Response of Nonclassically Damped Mechanical Systems

Abstract

Selected recent literature is surveyed on several topics pertaining to the time response of a discrete, time-invariant, linear, multiple degree-of-freedom mechanical system. These topics have been the subjects of extensive recent investigation, and are believed to be useful in design, modeling and computational simulation. Attention is restricted to systems with nonclassical damping, by which is meant that the systems do not observe classical normal modes. Several specific results are described in some detail. Topics covered include conditions for asymptotic stability, conditions for underdamping and overdamping, localization of system eigenvalues, and response bounds under various types of excitations. The final topic presented is the relation between system stability and the numerical stability of time integration methods used to calculate the system time response.