عنوان

Nonlinear Oscillations in Mechanical Engineering

3540281169

9783540281160

b550208

Nonlinear Oscillations in Mechanical Engineering

[Book]

by Alexander Fidlin.

Berlin, Heidelberg

Springer-Verlag Berlin Heidelberg

2006

Titre de l'écran-titre (visionné le 2 juillet 2008).

Title Page --;Preface --;Contents --;1. Introduction --;1.1. Usual Sources of Nonlinearity in Mechanical Engineering --;1.1.1 Geometrical Nonlinearities --;1.1.2 Physical Nonlinearities --;1.1.3 Structural or Designed Nonlinearities --;1.1.4 Constraints --;1.1.5 Nonlinearity of Friction --;1.2 The Basic Ideas of the Perturbation Analysis --;1.2.1 Variation of Free Constants and Systems in the Standard Form --;1.2.2 Standard Averaging as an Almost Identical Transformation --;1.2.3 Method of Multiple Scales --;1.2.4 Direct Separation of Motions --;1.2.5 Relationship between These Methods --;1.3 Examples of Elementary Nonlinear Problems Solved by Standard --;1.3.1 Instability and Self Excited Oscillations in the Van Der Pol's --;1.3.2 The Main Resonance in a System with a Small Cubic Nonlinearity --;1.3.3 Secondary Resonances in the System with Cubic Nonlinearity and --;1.4 Axiomatic Theory of Collisions --;1.4.1 Impulsive Motion of the Point Mass --;1.4.2 Impulsive Motion of a System of Point Masses --;1.4.3 Impulsive Motion of a Rigid Body --;1.4.4 Collinear Collision of Two Point Masses --;1.4.5 Direct Collisions in Mechanical Systems with Ideal Constraints --;1.4.6 Concluding Remarks --;2. Oscillations in Systems with Dry Friction --;2.1 Self Excited Oscillations of the Mass-on-Moving-Belt --;2.1.1 The Problem Description; Equations of Motion --;2.1.2 Types of Motion --;2.1.3 Pure Slip Oscillations --;2.1.4 Stick-slip Oscillations --;2.1.5 Discussion of the Results --;2.1.6 Concluding Remarks --;2.2 Friction Induced Flutter --;2.2.1 Mathematical Basics of Flutter in a System with Two Degrees of --;2.2.2 Wobbling of an Elastically Supported Friction Disc --;2.2.3 On the Unstable Behavior of an Asymmetrically Supported Disc --;2.2.4 Conclusions --;2.3 Vibration Induced Displacement. Averaging in Discontinuous Systems --;2.3.1 A Simple Example of the Vibration Induced Displacement --;2.3.2 Mathematical Basics for the First Order Averaging of the Constant --;2.3.3 The Elementary Example of the Vibration Induced Displacement. --;2.3.4 Discussion of the Results --;2.3.5 Conclusions --;2.4 Vibration Induced Displacement of a Resonant Friction Slider --;2.4.1 Problem Description --;2.4.2 Equations of Motion --;2.4.3 Illustration to System's Behavior --;2.4.4 Transformation to the Principal Form. Amplitude of the Resonator --;2.4.5 Motion of the Slider: Preparing for Averaging --;2.4.6 Performance in Dependence of Parameters; Comparison etween --;2.4.7 Conclusions --;3. Systems with Almost Elastic Collisions --;3.1 The Basic Ideas of Discontinuous Averaging. Unfolding --;3.1.1 The Basic Idea of the Unfolding Transformation for the Mass --;3.1.2 The Unfolding Transformation and Averaging in Case of Slightly --;3.1.3 Comparison between Analytic and Numeric Predictions for the --;3.1.4 Unfolding Transformation and Averaging for the Free Mass in a --;3.2. The "Mass-on-Moving-Belt" Limited at One Side: First Order --;3.3. Second Order Approximation in Systems with Almost Elastic --;3.3.1 General Mathematical Approach --;3.3.2 The Second Order Approximation for the Amplitude of the Mass --;3.3.3 Discussion of the Results and Comparisons with Numeric --;3.4. The "Mass on Moving Belt" in a clearance --;3.4.1 The Gov.

Engineering.

Mechanics.

Vibration.

by Alexander Fidlin.

Alexander Fidlin

[Book]

Y