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Regular and chaotic vibrations in selected systems with pendulums
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  • Regular and chaotic vibrations in selected systems with pendulums
ID: 138978
Sado Danuta
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Author: Sado Danuta
ISBN: 978-83-204-3676-1
Publisher: WNT Scientific and Technical Publishers
Publication year: 2010
Format: B5
Pages: 198
Paperback

About the book

The book is devoted to the phenomena of transferring vibrations between elements of work machines containing pendulums. The problem of transmission of vibrations is important, because the system set in vibrations of a certain form can arouse vibrations of another form, sometimes difficult to predict, which can lead to machine failure.
The book discusses the analytical and numerical studies of selected systems with pendulums with two and three degrees of freedom, which show in which conditions the vibrations can be transmitted and what character they may have and how this type of vibration can be controlled. On our publishing market there is a book that comprehensively covers the problem of regular and chaotic vibrations of autoparametric systems. This publication will probably fill this gap.
The book is intended for research workers of technical universities and research institutes as well as PhD students and engineers designing and operating machines and technical devices containing pendulums, as well as students of higher years of mechanical faculties.

Table of Contents


1.         PRELIMINARY NEWS
1.1.      Introduction
1.2.      Test methods for systems containing pendulums
1.2.1.    The method of many time scales.
1.2.2.    Examination of the nature of vibrations - regular and chaotic vibrations


2.         VIBRATION OF CIRCUIT ARRANGEMENTS WITH TWO DEGREES
          FREEDOMS, WHICH CONTAINS THE PENDANTS
2.1 ..         A springy pendulum
2.1.1.       Model of the system. Traffic equations
2.1.2.       Analytical studies using a multiple time scale
2.1.3        Numerical research
2.1.3.1.   Free vibrations of the springing pendulum
2.1.3.2.   The oscillation of the springing pendulum is forced by horizontal harmonic force
2.2.       Two pendulums connected in series (double pendulum)
2.2.1.     Model of the system. Traffic equations
2.2.2.       Analytical studies using a multiple time scale
2.2.3.      Numerical research
2.2.3.1.   Energy transfer conditions for free vibrations
2.2.3.2.   Regular and chaotic vibrations of a system forced by horizontal force
           harmonic
2.3.       Two pendulums connected by a spring
2.3.1.      Model of the system. Traffic equations
2.3.2.     Analytical studies using a multiple time scale
2.3.3.     Numerical research
2.3.3.1.   Numerical tests of free vibrations
2.3.3.2.   Numerical tests of forced vibrations - regular and chaotic vibrations
2.4.       Oscillator 7 suspended pendulum
2.4.1.      Model of the system. Traffic equations
2.4.2.     Analytical studies using a multiple time scale
2.4.2.1.   External resonance p, = 1 and internal resonance   β = 0.5
2.4.3.     Numerical research
2.4.3.1.   Numerical tests of free vibrations
2.4.3.2.   Numerical research of vibrations forced by vertical harmonic force
2.4.3.3.   Numerical research of vibrations forced by horizontal harmonic force



3.         MODELING OF FORCE - FORGOT IDEAL OR
          FORCED EXTREME
3.1.       Introduction
3.2.        System description. Traffic equations
3.2.1.     Equations of motion of the system with perfect excitation
3.2.2.     Equations of system motion with non-ideal extortion
3.3.       Analytical studies using a multiple time scale
3.4.       Numerical research
3.4.1.     Free vibrations of the ideal system
3.4.2.     Vibrations forced by the ideal system
3.4.3.     Forced vibrations of the non-ideal system



4.            VIBRATION OF AUTOPARAMETRIC ARRANGEMENTS WITH THREE DEGREES
FREEDOM
4.1.         Oscillator with a spring pendulum
4.1.1.      System description. Traffic equations
4.1.2. Numerical research
4.1.2.1.   Numerical tests of free vibrations
4.1.2.2.   Numerical studies of regular and chaotic vibrations
4.2.          Vibrations of a system consisting of an oscilator and a double pendulum
4.2.1.      Model of the system. Traffic equations
4.2.2.       Analytical studies using a multiple time scale
4.2.2.1.   Method of solution
4.2.2.2.   Analysis of vibrations for internal resonances 2 «2 = 1 / ah-o> 2 = 1 and
              external resonance / 7 = 1
4.2.3.      Numerical research
4.2.3.1.   Numerical examination of free vibrations
4.2.3.2.   Numerical examination of regular and chaotic vibrations
4.3.          Vibrations of the autoparametric system with two pendulums connected by a spring
4.3.1.     Model of the system. Traffic equations
4.3.2.     Analytical studies using a multiple time scale
4.3.3.     Numerical research
4.3.3.1. Numerical tests of free vibrations
4.3.3.2. Numerical research of vibrations forced by vertical harmonic force



5.          APPLICATION OF MATERIALS WITH MEMORIAL MEMORY (SMA) W.
        AUTOPARAMETRIC ARRANGEMENTS
5.1.       Introduction
5.2.       Use of shape memory (SMA) materials to control vibrations
in autoparametric systems
5.2.1.     Model of the system. Traffic equations
5.2.2.     Numerical research
5.2.2.1. Influence of spring with SMA on free vibrations
5.2.2.2. Influence of spring with SMA on forced vibrations
5.3.        Pseudo-elastic effect in the autoparametric system with a spring with SMA
5.3.1.      System description. Traffic equations
5.3.2.       Numerical research _
5.3.2.1.   The pseudo-elastic effect in free vibrations
5.3.2.2.   The pseudo elasticity effect in forced oscillations

BIBLIOGRAPHY
INDEX


 



 

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