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This textbook presents the motion of pure nonlinear oscillatory
systems and various solution procedures which give the approximate
solutions of the strong nonlinear oscillator equations. It presents
the author's original method for the analytical solution procedure
of the pure nonlinear oscillator system. After an introduction, the
physical explanation of the pure nonlinearity and of the pure
nonlinear oscillator is given. The analytical solution for free and
forced vibrations of the one-degree-of-freedom strong nonlinear
system with constant and time variable parameters is considered. In
this second edition of the book, the number of approximate solving
procedures for strong nonlinear oscillators is enlarged and a
variety of procedures for solving free strong nonlinear oscillators
is suggested. A method for error estimation is also given which is
suitable to compare the exact and approximate solutions. Besides
the oscillators with one degree-of-freedom, the one and two mass
oscillatory systems with two-degrees-of-freedom and continuous
oscillators are considered. The chaos and chaos suppression in
ideal and non-ideal mechanical systems is explained. In this second
edition more attention is given to the application of the suggested
methodologies and obtained results to some practical problems in
physics, mechanics, electronics and biomechanics. Thus, for the
oscillator with two degrees-of-freedom, a generalization of the
solving procedure is performed. Based on the obtained results,
vibrations of the vocal cord are analyzed. In the book the
vibration of the axially purely nonlinear rod as a continuous
system is investigated. The developed solving procedure and the
solutions are applied to discuss the muscle vibration. Vibrations
of an optomechanical system are analyzed using the oscillations of
an oscillator with odd or even quadratic nonlinearities. The
extension of the forced vibrations of the system is realized by
introducing the Ateb periodic excitation force which is the series
of a trigonometric function. The book is self-consistent and
suitable for researchers and as a textbook for students and also
professionals and engineers who apply these techniques to the field
of nonlinear oscillations.
In this book the dynamics of the non-ideal oscillatory system, in
which the excitation is influenced by the response of the
oscillator, is presented. Linear and nonlinear oscillators with one
or more degrees of freedom interacting with one or more energy
sources are treated. This concerns for example oscillating systems
excited by a deformed elastic connection, systems excited by an
unbalanced rotating mass, systems of parametrically excited
oscillator and an energy source, frictionally self-excited
oscillator and an energy source, energy harvesting system, portal
frame - non-ideal source system, non-ideal rotor system, planar
mechanism - non-ideal source interaction. For the systems the
regular and irregular motions are tested. The effect of
self-synchronization, chaos and methods for suppressing chaos in
non-ideal systems are considered. In the book various types of
motion control are suggested. The most important property of the
non-ideal system connected with the jump-like transition from a
resonant state to a non-resonant one is discussed. The so called
'Sommerfeld effect', resonant unstable state and jumping of the
system into a new stable state of motion above the resonant region
is explained. A mathematical model of the system is solved
analytically and numerically. Approximate analytical solving
procedures are developed. Besides, simulation of the motion of the
non-ideal system is presented. The obtained results are compared
with those for the ideal case. A significant difference is evident.
The book aims to present the established results and to expand the
literature in non-ideal vibrating systems. A further intention of
the book is to give predictions of the effects for a system where
the interaction between an oscillator and the energy source exist.
The book is targeted at engineers and technicians dealing with the
problem of source-machine system, but is also written for PhD
students and researchers interested in non-linear and non-ideal
problems.
In this book the dynamics of the non-ideal oscillatory system, in
which the excitation is influenced by the response of the
oscillator, is presented. Linear and nonlinear oscillators with one
or more degrees of freedom interacting with one or more energy
sources are treated. This concerns for example oscillating systems
excited by a deformed elastic connection, systems excited by an
unbalanced rotating mass, systems of parametrically excited
oscillator and an energy source, frictionally self-excited
oscillator and an energy source, energy harvesting system, portal
frame - non-ideal source system, non-ideal rotor system, planar
mechanism - non-ideal source interaction. For the systems the
regular and irregular motions are tested. The effect of
self-synchronization, chaos and methods for suppressing chaos in
non-ideal systems are considered. In the book various types of
motion control are suggested. The most important property of the
non-ideal system connected with the jump-like transition from a
resonant state to a non-resonant one is discussed. The so called
'Sommerfeld effect', resonant unstable state and jumping of the
system into a new stable state of motion above the resonant region
is explained. A mathematical model of the system is solved
analytically and numerically. Approximate analytical solving
procedures are developed. Besides, simulation of the motion of the
non-ideal system is presented. The obtained results are compared
with those for the ideal case. A significant difference is evident.
The book aims to present the established results and to expand the
literature in non-ideal vibrating systems. A further intention of
the book is to give predictions of the effects for a system where
the interaction between an oscillator and the energy source exist.
The book is targeted at engineers and technicians dealing with the
problem of source-machine system, but is also written for PhD
students and researchers interested in non-linear and non-ideal
problems.
This textbook presents the motion of pure nonlinear oscillatory
systems and various solution procedures which give the approximate
solutions of the strong nonlinear oscillator equations. It presents
the author's original method for the analytical solution procedure
of the pure nonlinear oscillator system. After an introduction, the
physical explanation of the pure nonlinearity and of the pure
nonlinear oscillator is given. The analytical solution for free and
forced vibrations of the one-degree-of-freedom strong nonlinear
system with constant and time variable parameters is considered. In
this second edition of the book, the number of approximate solving
procedures for strong nonlinear oscillators is enlarged and a
variety of procedures for solving free strong nonlinear oscillators
is suggested. A method for error estimation is also given which is
suitable to compare the exact and approximate solutions. Besides
the oscillators with one degree-of-freedom, the one and two mass
oscillatory systems with two-degrees-of-freedom and continuous
oscillators are considered. The chaos and chaos suppression in
ideal and non-ideal mechanical systems is explained. In this second
edition more attention is given to the application of the suggested
methodologies and obtained results to some practical problems in
physics, mechanics, electronics and biomechanics. Thus, for the
oscillator with two degrees-of-freedom, a generalization of the
solving procedure is performed. Based on the obtained results,
vibrations of the vocal cord are analyzed. In the book the
vibration of the axially purely nonlinear rod as a continuous
system is investigated. The developed solving procedure and the
solutions are applied to discuss the muscle vibration. Vibrations
of an optomechanical system are analyzed using the oscillations of
an oscillator with odd or even quadratic nonlinearities. The
extension of the forced vibrations of the system is realized by
introducing the Ateb periodic excitation force which is the series
of a trigonometric function. The book is self-consistent and
suitable for researchers and as a textbook for students and also
professionals and engineers who apply these techniques to the field
of nonlinear oscillations.
This book deals with the problem of dynamics of bodies with
time-variable mass and moment of inertia. Mass addition and mass
separation from the body are treated. Both aspects of mass
variation, continual and discontinual, are considered. Dynamic
properties of the body are obtained applying principles of
classical dynamics and also analytical mechanics. Advantages and
disadvantages of both approaches are discussed. Dynamics of
constant body is adopted, and the characteristics of the mass
variation of the body is included. Special attention is given to
the influence of the reactive force and the reactive torque. The
vibration of the body with variable mass is presented. One and two
degrees of freedom oscillators with variable mass are discussed.
Rotors and the Van der Pol oscillator with variable mass are
displayed. The chaotic motion of bodies with variable mass is
discussed too. To support learning, some solved practical problems
are included.
This book deals with the problem of dynamics of bodies with
time-variable mass and moment of inertia. Mass addition and mass
separation from the body are treated. Both aspects of mass
variation, continual and discontinual, are considered. Dynamic
properties of the body are obtained applying principles of
classical dynamics and also analytical mechanics. Advantages and
disadvantages of both approaches are discussed. Dynamics of
constant body is adopted, and the characteristics of the mass
variation of the body is included. Special attention is given to
the influence of the reactive force and the reactive torque. The
vibration of the body with variable mass is presented. One and two
degrees of freedom oscillators with variable mass are discussed.
Rotors and the Van der Pol oscillator with variable mass are
displayed. The chaotic motion of bodies with variable mass is
discussed too. To support learning, some solved practical problems
are included.
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