This book expounds the theory of non-linear vibrations, a topic of great interest at present because of its many applications to important fields in physics and engineering. After introducing chapters giving the basic techniques for the study of non-linear systems the authors develop in detail the theory of selected topics encountered in their own work, presenting original material, approaches and results of analysis, and providing illustrations of useful applications.
Fur einen Rotor mit elastischer Halterung in axialer wie auch seitlicher Richtung wird ein Modell formuliert, das auf das Stabilitutsproblem fur kleine Vertikalschwingungen in senkrechter Position fihrt. Dies ist ein autopurametrisches Erregungsproblem, das in Gestalt zweier gekoppelter Mathieu-iihnlicher Gleichungen formuliert werden kann. Die Analyse der Speziulfille ohne und mit (hearer) Dampfung sowie der Full nichtlinearer Dampfung werden ausgefuhrt, wobei Mittelung und numerische Bijiurkationstechniken angewendet werden, die im nichtlinearen Fall auf Hysteresis und Phasensynchronisierung fiihren. A model is formulated for a rotor with elastic support in axial and lateral directions which leads to the problem of stability of small vertical oscillations in the upright position. This is an autoparametric excitation problem which can be formulated as two coupled Mathieu-like equations. The analysis of the cases without and with (linear) damping and the case of nonlinear damping is carried out using averaging and numerical bifurcation techniques leading in the nonlinear case to hysteresis and phase-locking. MSC (1980): 70E05,
Abstract. Two different models for simulating the ship motion in longitudinal or oblique seas are presented and studied in detail. Particular attention is devoted to the parametrically induced rolling which may be established by means of the nonlinear coupling between both heave-roll and/or pitch-roll motions. It is proved that the phenomenon is likely to occur with this mechanism when the roll frequency is subharmonic of the encounter wave frequency and when the vertical motions become resonant.
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