Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1976 · 49 citations · 3 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsVibrationDissipative SystemsForced VibrationFree VibrationNonlinear DynamicsStability TheoryTransient VibrationConservative Dynamical SystemsFree Vibration ResponseHarmonic OscillatorsHarmonic ResponseNonlinear Free VibrationPositive DefinitenessStability Of Free VibrationsTransient Stability Of Vibrating Systems
Abstract A number of results are presented, relating to the matrix equation Aq̣̈ + Bq̇ + Cq = Q(t). It is not assumed that the system matrices A, B and C possess any of the familiar properties (of symmetry, skew symmetry or positive definiteness). These results relate to free motion in which Q(t) = 0, to forced harmonic motion in which Q(t) = ϕ eiωt and to transient vibration in which Q(t) is an arbitrary function of time.
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Classical Normal Modes in Damped Linear Dynamic Systems
T. K. Caughey · Journal of Applied Mechanics · 1960 · 385 citations