Rectified Rotary Vibration in Two-Degree-of-Freedom and in Single-Degree-of-Freedom Gyros

1963 ◽  
pp. 247-258 ◽  
Author(s):  
J. Stanley Ausman
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Two Degree Of Freedom ◽  
Rotary Vibration

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

Chaotic Responses of a Two-Degree-of-Freedom Elastic-Plastic Beam Model to Short Pulse Loading

1992 ◽  
Vol 59 (4) ◽  
pp. 711-721 ◽  
Author(s):  
J.-Y. Lee ◽  
P. S. Symonds ◽  
G. Borino
Keyword(s):  
Short Pulse ◽  
Direct Method ◽  
Degree Of Freedom ◽  
Beam Model ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Arch Action ◽  
Time Histories ◽  
Energy Plane ◽  
Two Degree Of Freedom

The paper discusses chaotic response behavior of a beam model whose ends are fixed, so that shallow arch action prevails after moderate plastic straining has occurred due to a short pulse of transverse loading. Examples of anomalous displacement-time histories of a uniform beam are first shown. These motivated the present study of a two-degree-of-freedom model of Shanley type. Calculations confirm these behaviors as symptoms of chaotic unpredictability. Evidence of chaos is seen in displacement-time histories, in phase plane and power spectral diagrams, and especially in extreme sensitivity to parameters. The exponential nature of the latter is confirmed by calculations of conventional Lyapunov exponents and also by a direct method. The two-degree-of-freedom model allows use of the energy approach found helpful for the single-degree-of-freedom model (Borino et al., 1989). The strain energy is plotted as a surface over the displacement coordinate plane, which depends on the plastic strains. Contrasting with the single-degree-of-freedom case, the energy diagram illuminates the possibility of chaotic vibrations in an initial phase, and the eventual transition to a smaller amplitude nonchaotic vibration which is finally damped out. Properties of the response are further illustrated by samples of solution trajectories in a fixed total energy plane and by related Poincare section plots.

Graphical Methods to Locate the Secondary Instant Centers of Single-Degree-of-Freedom Indeterminate Linkages

2005 ◽  
Vol 127 (2) ◽  
pp. 249-256 ◽  
Author(s):  
David E. Foster ◽  
Gordon R. Pennock
Keyword(s):  
Degree Of Freedom ◽  
Graphical Methods ◽  
Single Degree Of Freedom ◽  
Revolute Joint ◽  
Single Degree ◽  
Revolute Joints ◽  
Straight Line ◽  
Single Link ◽  
Prismatic Joints ◽  
Two Degree Of Freedom

This paper presents graphical techniques to locate the unknown instantaneous centers of zero velocity of planar, single-degree-of-freedom, linkages with kinematic indeterminacy. The approach is to convert a single-degree-of-freedom indeterminate linkage into a two-degree-of-freedom linkage. Two methods are presented to perform this conversion. The first method is to remove a binary link and the second method is to replace a single link with a pair of links connected by a revolute joint. First, the paper shows that a secondary instant center of a two-degree-of-freedom linkage must lie on a unique straight line. Then this property is used to locate a secondary instant center of the single-degree-of-freedom indeterminate linkage at the intersection of two lines. The two lines are obtained from a purely graphical procedure. The graphical techniques presented in this paper are illustrated by three examples of single-degree-of-freedom linkages with kinematic indeterminacy. The examples are a ten-bar linkage with only revolute joints, the single flier eight-bar linkage, and a ten-bar linkage with revolute and prismatic joints.

Graphical Methods to Locate the Secondary Instant Centers of Single-Degree-of-Freedom Indeterminate Linkages

2004 ◽  
Author(s):  
David E. Foster ◽  
Gordon R. Pennock
Keyword(s):  
Degree Of Freedom ◽  
Graphical Methods ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Revolute Joints ◽  
Straight Line ◽  
Single Link ◽  
Prismatic Joints ◽  
Instantaneous Center ◽  
Two Degree Of Freedom

This paper presents graphical techniques to locate the unknown instantaneous centers of zero velocity of planar, single-degree-of-freedom, linkages with kinematic indeterminacy. The approach is to convert a single-degree-of-freedom indeterminate linkage into a two-degree-of-freedom linkage. Two methods are presented to perform this conversion. The first method is to remove a binary link and the second method is to replace a single link with a pair of links connected by a revolute joint. First, the paper shows that a secondary instantaneous center of a two-degree-of-freedom linkage must lie on a unique straight line. Then this property is used to locate a secondary instant center of the single-degree-of-freedom linkage at the intersection of two lines. The two lines are obtained from a purely graphical procedure. The graphical techniques presented in this paper are illustrated by three examples of single-degree-of-freedom linkages with kinematic indeterminacy. The examples are a ten-bar linkage with only revolute joints, the single flier eight-bar linkage, and a ten-bar linkage with revolute and prismatic joints.

scholarly journals Higher order stochastic averaging method for mechanical systems having two degrees of freedom

2004 ◽  
Vol 26 (2) ◽  
pp. 103-110
Author(s):  
Nguyen Duc Tinh
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Higher Order ◽  
Degree Of Freedom ◽  
Approximation Solution ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Two Degree Of Freedom

Higher order stochastic averaging method is widely used for investigating single-degree-of-freedom nonlinear systems subjected to white and coloured random noises.In this paper the method is further developed for two-degree-of-freedom systems. An application to a system with cubic damping is considered and the second approximation solution to the Fokker-Planck (FP) equation is obtained.

Vibration Control of Structures by Using Multi-Degree-of-Freedom Dynamic Absorber

2004 ◽  
Author(s):  
Daisuke Iba ◽  
Akira Sone ◽  
Arata Masuda
Keyword(s):  
Output Feedback Control ◽  
Degree Of Freedom ◽  
Vibration Modes ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Bilinear Matrix Inequality ◽  
Static Output Feedback Control ◽  
Dynamic Absorber ◽  
Two Degree Of Freedom ◽  
Static Output

This paper proposes a multi-degree-of-freedom dynamic absorber, which has multiple auxiliary masses and can suppress multiple vibration modes of structures passively during earthquake. The designable parameters of the dynamic absorber are determined by utilizing a theory of H∞ static output feedback control and by solving a Bilinear-Matrix-Inequality (BMI) problem. Finally, numerical simulations for the two-degree-of-freedom dynamic absorber show the advantages of the proposed method compared with the conventional single-degree-of-freedom dynamic absorber.

Analysis and Design of a Two Degree of Freedom Hoeckens-Pantograph Leg Mechanism

2015 ◽  
Author(s):  
Dmitri Fedorov ◽  
Lionel Birglen
Keyword(s):  
Screw Theory ◽  
Degree Of Freedom ◽  
Performance Indices ◽  
Single Degree Of Freedom ◽  
Analysis And Design ◽  
Single Degree ◽  
Compliant Joints ◽  
Two Degree Of Freedom ◽  
Novel Design ◽  
Limited Motion

Hoeckens and Chebychev linkages have been widely discussed in the literature as design solutions to build single degree of freedom (DOF) leg mechanisms. Compared to fully actuated legs, often bio-inspired, they offer an unmatched simplicity. However, due to their limited motion capability, they can only be used when the traversed terrain is of limited difficulty. In order to alleviate this drawback, a novel design with a second DOF is proposed in this paper. The introduced mechanism is composed of a Hoeckens linkage augmented by a Pantograph for which the position of the pivot can be changed through an additional rotating link. Screw theory is used to determine the kinematic equations of the mechanism, its singular configurations, and its attainable workspace. Subsequently, an optimization of the geometric parameters is performed to maximize performance indices pertaining to the size of the mechanism’s workspace. Finally, possible use of compliant joints is discussed.

Understanding Damping in Linear Multi-Degree of Freedom Systems

2014 ◽  
Author(s):  
Hugh Goyder
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Acoustic Modes ◽  
Single Degree ◽  
Modes Of Vibration ◽  
Damping Effects ◽  
Two Degree Of Freedom ◽  
Straightforward Extension

A system with damping is much more difficult to model than an undamped system. In particular, the effect of damping on a multi-degree-of-freedom system is not a straightforward extension of the damped found in single-degree-of-freedom systems. The complications of a multi-degree-of-freedom system are first examined by investigating the acoustic modes of a pipe with energy leaking from one boundary. This system can be modelled exactly. It is found that individual modes of vibration cannot be separated and are always coupled by damping effects which may involve some modes being active and not passive. Furthermore if damping sinks are increased the damping ratios can either increase or decrease. The damping of systems with fewer degrees-of-freedom are then examined to determine how damping coupling behaves. It is found that a two-degree-of-freedom system exhibits increasing and decreasing damping values as the magnitude of a damping sink is varied.

Analytical Prediction of Chatter Stability in Milling—Part II: Application of the General Formulation to Common Milling Systems

1998 ◽  
Vol 120 (1) ◽  
pp. 31-36 ◽  
Author(s):  
E. Budak ◽  
Y. Altintas¸
Keyword(s):  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Analytical Prediction ◽  
Chatter Stability ◽  
Peripheral Milling ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Chatter Prediction ◽  
Milling Chatter ◽  
Two Degree Of Freedom

The general formulation for the milling chatter prediction developed in Part I of the paper is applied to common milling systems. Three cases are considered: a workpiece with single-degree-of-freedom, a face milling cutter with two-degree-of-freedom, and peripheral milling of a cantilevered thin web. The general milling stability formulation is further simplified for the less complicated models. For each case, an analytical expression which explicitly relate the chatter limit to the milling conditions and tool-workpiece dynamics are derived. The analytical predictions are compared with numerical and time domain solutions proposed by previous research. It is shown that the proposed method can accurately predict the chatter limits in milling and thus eliminates the time consuming numerical solutions.

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