On the Influence of Damping on the Stability of Certain Gyroscopic Systems

1978 ◽  
pp. 14-24
Author(s):  
H. Brauchli
Keyword(s):  
The Stability ◽  
Gyroscopic Systems

Parametric Stability of a Nonlinear Rotating Blade

2013 ◽  
Author(s):  
Fengxia Wang ◽  
Albert C. J. Luo
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Parametric Stability ◽  
Rotating Blade ◽  
Geometric Term ◽  
Stability And Bifurcations ◽  
The Stability ◽  
The Galerkin Method ◽  
Gyroscopic Systems ◽  
Generalized Harmonic Balance Method

The stability of period-1 motions of a rotating blade with geometric nonlinearity is studied. The roles of cubic stiffening geometric term are considered in the study of nonlinear periodic motions and its stability and bifurcations of a rotating blade. The nonlinear model of a rotating blade is reduced to the ordinary differential equations through the Galerkin method, and the gyroscopic systems with parametric excitations are obtained. The generalized harmonic balance method is employed to determine the period-1 solutions and the corresponding stability and bifurcations.

On the stability of linear conservative gyroscopic systems

1983 ◽  
Vol 34 (6) ◽  
pp. 807-815 ◽  
Author(s):  
K. Huseyin ◽  
P. Hagedorn ◽  
W. Teschner
Keyword(s):  
The Stability ◽  
Gyroscopic Systems

A Sufficient Stability Condition for Linear Conservative Gyroscopic Systems

1994 ◽  
Vol 61 (3) ◽  
pp. 715-717 ◽  
Author(s):  
Jinn-Wen Wu ◽  
Tsu-Chin Tsao
Keyword(s):  
Stability Condition ◽  
Entire System ◽  
Stiffness Matrices ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Stability ◽  
Gyroscopic Systems

A sufficient stability condition for linear conservative gyroscopic systems with negative definite stiffness matrices is given. The condition for the stability is stated in terms of the coefficients of system matrices without solving the spectrum of the entire system. An example is given for comparison with existing results.

On the Stability Criteria for Conservative Gyroscopic Systems

1991 ◽  
Vol 113 (1) ◽  
pp. 58-61 ◽  
Author(s):  
K. Huseyin
Keyword(s):  
Dynamical System ◽  
Stability Criteria ◽  
Scalar Parameter ◽  
Scope Of Application ◽  
The Stability ◽  
Gyroscopic Systems ◽  
New Criteria

Two alternative but equivalent stability criteria for linear conservative gyroscopic systems are presented. The development of the criteria is based on the concept of symmetrizability associated with general matrices, and the results are in terms of the matrices describing the dynamical system. Although the new criteria involves a scalar parameter, the restrictions associated with an earlier result are removed, and the scope of application is broadened. An illustrative example is presented.

On the Stability of Gyroscopic Systems

1998 ◽  
Vol 65 (2) ◽  
pp. 519-522 ◽  
Author(s):  
P. Lancaster ◽  
P. Zizler
Keyword(s):  
Equilibrium Position ◽  
Stiffness Matrix ◽  
Necessary Condition ◽  
Negative Eigenvalues ◽  
The Stability ◽  
Gyroscopic Systems

Gyroscopic systems considered here have the form Ay¨ + Gy˙ + Ky = 0 where A, G, K are real n × n matrices with A > O, GT = −G, KT = K, and the stiffness matrix K has some negative eigenvalues; i.e., the equilibrium position is unstable (when G = 0). A new necessary condition for stability is established. It is also shown that gyroscopic systems with K < 0 and G singular are always unstable for G sufficiently large.

A Sufficient Condition for the Stability of Conservative Gyroscopic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 895-898 ◽  
Author(s):  
D. J. Inman
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Sufficient Condition ◽  
Design Constraints ◽  
The Stability ◽  
Gyroscopic Systems

A sufficient condition for the stability of conservative gyroscopic systems with negative definite stiffness is presented. The conditions for stability are stated in terms of the definiteness of certain combinations of the coefficient matrices of the equations of motion. These conditions yield design constraints in terms of the physical parameters of the system. An example is given to illustrate the correctness of the result, as well as to provide a comparison with the results of other researchers.

Stability of Linear Conservative Gyroscopic Systems

1991 ◽  
Vol 58 (1) ◽  
pp. 229-232 ◽  
Author(s):  
J. A. Walker
Keyword(s):  
Sufficient Conditions ◽  
Design Constraints ◽  
Stability And Instability ◽  
The Stability ◽  
Gyroscopic Systems

Sufficient conditions are obtained for the stability and instability of linear conservative gyroscopic systems. The conditions are nonspectral, involve only the definiteness of certain combinations of the coefficient matrices, and may yield useful design constraints. An example is employed to compare these results with earlier results of the same type.

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