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E-raamat: Dynamics of Machines with Variable Mass

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Dynamics of Machines with Variable MassSuurem pilt
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Presents certain theories in the dynamics of systems with variable mass that can be used to find solutions to many problems in machines and mechanisms with time variable parameters. Various types of machines are considered, such as centrifuges, sieves for sorting particles, transportation mechanisms, lifting mechanisms, cranes, automatic weight measuring instruments, and rotors used in the textile, cable and paper industries. The book considers both weak and strong nonlinear vibrations, and discusses chaotic phenomena. The conservation laws and adiabatic invariants for systems with variable mass are formulated, and the stability and instability conditions of motion are defined. Annotation c. by Book News, Inc., Portland, Or.

Designed to be a complete and integrated text on the dynamic properties of machines, mechanisms, and rotors with variable mass, this book presents new results from investigations based on the general dynamics of systems with variable parameters. The book considers both weak and strong nonlinear vibrations of these systems, and chaotic phenomena are also discussed. The conservation laws and adiabatic invariants for systems with variable mass are formulated and the stability and instability conditions of motion are defined.
Introduction to the Series xi
Preface xiii
Machines with Variable Mass
Introduction
1(1)
Mechanisms with variable mass
1(7)
Rotors with variable mass
8(4)
Comments and references
12(3)
General Principles of Dynamics of Systems with Variable Mass
Introduction
15(1)
Dynamics of particles with variable mass
15(6)
Dynamics of a system of particles with variable mass
21(6)
Dynamics of bodies with variable mass
27(6)
Mathematical models of mechanisms and rotors with variable parameters
33(6)
Comments and references
39(2)
Vibrations in Machines with Small Nonlinearities and with Parameters which Vary with Time
Introduction
41(1)
Free vibrations of one-degree-of-freedom mechanisms with time variable parameters
42(2)
Vibrations of wagon-measuring mechanisms
44(2)
Free vibrations of single mass systems with two-degrees-of-freedom
46(5)
Vibrations of rotors with variable mass
51(19)
Forced vibrations of a single mass system with two-degrees-of-freedom
70(5)
Comments and references
75(2)
Vibrations of Machines with Time Variable Parameters and Strong Nonlinearity
Introduction
77(1)
Vibrations of one-degree-of-freedom oscillators with time variable parameters
78(7)
Vibrations of a system with a complex deflection function and strong quasi-cubic nonlinearity
85(1)
Vibrations of a centrifuge with variable mass
86(3)
Cubic nonlinear systems with slowly varying parameters and complex deflection functions
89(5)
Vibrations of a rotor with a winding band
94(4)
Comments and references
98(1)
Chaos in Systems with Time Variable Parameters
Introduction
99(1)
Melnikov's criteria for chaos applied to systems with time variable parameters
99(3)
Chaos in one-degree-of-freedom systems with variable mass
102(7)
Dynamic behaviour of a lifting crane mechanism
109(11)
Chaos in rotors with variable mass
120(6)
Comments and references
126(1)
Conservation Laws and Adiabatic Invariants for Systems with Variable Mass
Introduction
127(1)
Conservation laws of nonconservative Lagrange systems
128(3)
Conservation laws of systems with variable mass under the influence of a central force
131(6)
Conservation laws for purely nonconservative systems
137(3)
Conservation laws for vibrating machines with variable mass
140(3)
Conservation laws for sieve vibrations
143(1)
Adiabatic invariants for dynamic systems with one-degree-of-freedom
144(8)
Adiabatic invariants of quasi-pure-cubic oscillators
152(9)
Adiabatic invariants of dynamic systems with two-degrees-of-freedom
161(10)
Adiabatic invariants for strongly nonlinear dynamic systems described by a complex function
171(12)
Comments and references
183(2)
Stability of Motion of Machines with Variable Mass
Introduction
185(1)
The Lyapunov function. General criteria of Sylvester
185(2)
The Lyapunov direct method
187(4)
The influence of the impact force on the stability of motion for mechanisms with one-degree-of-freedom and variable mass
191(6)
Stability of rotation of a rotor with time-dependent parameters
197(5)
Stability of rotation of a symmetrical rotor with variable mass supported on bearings with clearance
202(5)
The stability of a clamped-free rotor with variable mass in the case of radial rubbing
207(7)
Comments and references
214(3)
References 217(16)
Index 233
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