Analysis of Parametrically Excited Large Vibration Systems.
Final technical rept. 1979-1983,
EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZURICH (SWITZERLAND) INST FUER MECHANIK
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Parametrically excited vibration systems are described by linear differential equations with periodic coefficients. The stability of such systems can be characterized by the stable and unstable regions in the plane of two significant system parameters epsilon and omega. Here, omega is preferably the fundamental frequency of the parametric excitation. The stability investigation of parametrically excited systems is based on the characteristic exponents or on the characteristic multipliers. Obtaining the stability chart by a pointwise analysis based on Floquet theory for a net of points meshed over the parameter plane is a very expensive computer task. The objective of this work is the reduction of this unbearable high computer time consumption by the combination of the Floquet theory, perturbation analysis and numerical methods. This analyticalnumerical method provides effective procedures for the stability investigation of large parametrically excited vibration systems.