Resonances and Instabilities in Dynamic Systems Incorporating a Cam

1981 ◽  
Vol 103 (4) ◽  
pp. 914-921
Author(s):  
D. L. Cronin ◽  
G. A. LaBouff
Keyword(s):  
Numerical Integration ◽  
Dynamic Systems ◽  
System Behavior ◽  
Kinematic Constraint ◽  
Approximate Methods ◽  
Motion Equations ◽  
Governing System ◽  
Resonant Behavior

A model consisting of two oscillators coupled through a kinematic constraint is employed in this paper to investigate resonances and instabilities in dynamic systems incorporating a cam. Examination of linearized motion equations exposes parameters governing system behavior. Explored using numerical integration, Floquet analyis, and approximate methods are coupling-induced modification of conventionally-predicted resonant behavior, and two categories of subharmonic and superharmonic instability. Approximate methods described in this paper for predicting resonances and instabilities appear to function reliably and offer the potential for reduced analysis cost.

scholarly journals Formulae for Numerical Differentiation

1941 ◽  
Vol 25 (263) ◽  
pp. 19-27 ◽  
Author(s):  
W G. Bickley
Keyword(s):  
Finite Difference ◽  
Numerical Integration ◽  
Numerical Differentiation ◽  
Companion Paper ◽  
Limited Range ◽  
Approximate Methods ◽  
Derivatives Of

In a recent paper (1) formulae were given for the numerical integration of a function in terms of its values at a set of arguments at equal intervals. In this companion paper, formulae for numerical differentiation, using the same data, are collected. Their utility in enabling derivatives of a function given numerically at such a set of arguments to be computed is obvious, the need arises in several approximate methods which are coming more and more into use (2), (3). The formulae avoid the labour of preliminary differencing, and are indeed more convenient than the finite difference formulae when the derivative is required at all the points of subdivision of a limited range.

Approximate methods of identifying dynamic systems

1992 ◽  
Vol 35 (7) ◽  
pp. 767-770
Author(s):  
I. V. Boikov ◽  
T. V. Cherusheva
Keyword(s):  
Dynamic Systems ◽  
Approximate Methods

Comparison of exact and approximate methods for analysing vibrational relaxation regions

1961 ◽  
Vol 10 (1) ◽  
pp. 33-47 ◽  
Author(s):  
P. A. Blythe
Keyword(s):  
Exact Solution ◽  
Shock Waves ◽  
Numerical Integration ◽  
Vibrational Relaxation ◽  
Relaxation Frequency ◽  
Rayleigh Line ◽  
Relaxation Equation ◽  
Approximate Methods ◽  
Exact And Approximate Methods

The validity of various solutions for the vibrational relaxation region in shock-waves, and of the assumptions on which they are based, has been assesed by comparison with an exact solution obtained by numerical integration of the relaxation equation, and also by use of the Rayleigh-line equations. Estimates of errors in the values of the relaxation frequency, determined by means of these solutions, are given.

Methods of chaos and self-organization in psychophysiology

10.12737/3394 ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 13-28
Author(s):  
Поскина ◽  
T. Poskina ◽  
Филатова ◽  
D. Filatova ◽  
Филатов ◽  
...  
Keyword(s):  
Phase Space ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Self Organization ◽  
Deterministic Approach ◽  
System Behavior ◽  
System Parameters ◽  
A Value ◽  
Identification Theory

. All the H. Haken’s postulates (1970-2013) emphasize deterministic approach and level a value of trajectory of behavior of biological dynamic system in phase space of states. The significance of the latter theory is hard to overestimate, because according to phase space of states the new identification theory is being created and behavioral descriptions of biological dynamic systems are given. This new theory is based on measures of biological dynamic system parameters in phase space of states and does not need any concrete equations, it can be based on detection of quasi-attractors’ parameters of biological dynamic system behavior in phase space of states and characters are quasi-attractor parameters.

scholarly journals Phase Shadows: An Enhanced Representation of Nonlinear Dynamic Systems

2017 ◽  
Vol 27 (14) ◽  
pp. 1730051
Author(s):  
Amalia Luque ◽  
Julio Barbancho ◽  
Javier Fernández Cañete ◽  
Antonio Córdoba
Keyword(s):  
Phase Portrait ◽  
Dynamic Systems ◽  
Limit Cycles ◽  
Nonlinear Dynamic ◽  
Equilibrium Points ◽  
Nonlinear Dynamic Systems ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
System Behavior ◽  
Cylindrical Phase

Many nonlinear dynamic systems have a rotating behavior where an angle defining its state may extend to more than 360[Formula: see text]. In these cases the use of the phase portrait does not properly depict the system’s evolution. Normalized phase portraits or cylindrical phase portraits have been extensively used to overcome the original phase portrait’s disadvantages. In this research a new graphic representation is introduced: the phase shadow. Its use clearly reveals the system behavior while overcoming the drawback of the existing plots. Through the paper the method to obtain the graphic is stated. Additionally, to show the phase shadow’s expressiveness, a rotating pendulum is considered. The work exposes that the new graph is an enhanced representational tool for systems having equilibrium points, limit cycles, chaotic attractors and/or bifurcations.

scholarly journals Numerical calculation of the transverse vibrations of the multispan beams for moving load

1997 ◽  
Vol 14 (3) ◽  
pp. 26-33
Author(s):  
Do Xuan Tho ◽  
Nguyen Van Khang
Keyword(s):  
Numerical Calculation ◽  
Numerical Integration ◽  
Moving Load ◽  
Suspension Bridges ◽  
Motion Equations ◽  
Transverse Vibrations ◽  
Ibm Pc

In this paper the numerical calculation of the transverse vibrations of the Multiplan beams for moving load is considered. A program has been worked out for the numerical integration of the motion equations on IBM-PC AT or XT. This program is useful in calculating the vibrations of the suspension bridges.

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