Reduction Methods for Nonlinear Vibrations of Spatially Continuous Systems with Initial Curvature

2000 ◽  
pp. 235-246 ◽  
Author(s):  
G. Rega ◽  
W. Lacarbonara ◽  
A. H. Nayfeh
Keyword(s):  
Nonlinear Vibrations ◽  
Continuous Systems ◽  
Initial Curvature ◽  
Reduction Methods

ON REGULAR AND IRREGULAR NONLINEAR VIBRATIONS IN TORSIONAL DISCRETE-CONTINUOUS SYSTEMS

2011 ◽  
Vol 21 (10) ◽  
pp. 3073-3082 ◽  
Author(s):  
AMALIA PIELORZ ◽  
DANUTA SADO
Keyword(s):  
Arbitrary Number ◽  
Nonlinear Vibrations ◽  
Rigid Bodies ◽  
Continuous Systems ◽  
Bifurcation Diagrams ◽  
Governing Equations ◽  
Mass System ◽  
The Third ◽  
Multimass System ◽  
Local Nonlinearity

The paper deals with regular and irregular nonlinear vibrations of discrete-continuous systems torsionally deformed. The systems consist of an arbitrary number of shafts connected by rigid bodies. In the systems, a local nonlinearity having a soft type characteristic is introduced. This nonlinearity is described by the polynomial of the third degree. General governing equations using the wave approach are derived for a multimass system. Detailed numerical considerations are presented for a two-mass system and a three-mass system. The possibility of occurrence of irregular vibrations is discussed on the basis of the Poincaré maps and bifurcation diagrams.

Chaotic Vibrations in Multi-Mass Discrete-Continuous Systems Torsionally Deformed with Local Nonlinearities

2014 ◽  
Vol 706 ◽  
pp. 6-13
Author(s):  
Amalia Pielorz ◽  
Danuta Sado
Keyword(s):  
Nonlinear Vibrations ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Numerical Results ◽  
Continuous Systems ◽  
Chaotic Motions ◽  
Chaotic Vibrations ◽  
Wave Approach ◽  
Escape Phenomenon ◽  
External Moment

The paper deals with nonlinear vibrations in discrete-continuous mechanical systems consisting of rigid bodies connected by shafts torsionally deformed with local nonlinearities having hard or soft characteristics. The systems are loaded by an external moment harmonically changing in time. In the study the wave approach is used. Numerical results are presented for three-mass systems. In the study of regular vibrations in the case of a hard characteristic amplitude jumps are observed while in the case of a soft characteristic an escape phenomenon is observed. Irregular vibrations, including chaotic motions, are found for selected parameters of the systems.

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