A Novel Type of Bi-Gyroscopic System Undergoing Both Rotating and Spinning Motions

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Ji-Hou Yang ◽  
Xiao-Dong Yang ◽  
Ying-Jing Qian ◽  
Wei Zhang
Keyword(s):  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Coupling Effect ◽  
Gyroscopic System ◽  
Complex Modes ◽  
Gyroscopic Coupling ◽  
Gyroscopic Systems

Abstract In order to explore the influence of combined gyroscopic coupling effect on the gyroscopic system, the dynamics of a beam undergoing both rotating and spinning motions as a bi-gyroscopic system is studied. The natural frequencies, modes, and stability of such a bi-gyroscopic system have been studied by the standard eigenvalue problems. The bifurcation series of frequencies and corresponding modal motions have been presented to show the gyroscopically coupled motions. The complex modes of the proposed bi-gyroscopic systems, such as whirling motions and in-plane reeling motions, have been illustrated.

Eigenvalue Inclusion Principles for Distributed Gyroscopic Systems

1992 ◽  
Vol 59 (3) ◽  
pp. 650-656 ◽  
Author(s):  
B. Yang
Keyword(s):  
Transfer Function ◽  
Discrete System ◽  
Natural Frequencies ◽  
Gyroscopic System ◽  
Positive Real ◽  
Constrained System ◽  
Function Formulation ◽  
Pointwise Constraints ◽  
Gyroscopic Systems ◽  
Vibrating Systems

In his famous treatise The Theory of Sound, Rayleigh enunciated an eigenvalue inclusion principle for the discrete, self-adjoint vibrating system under a constraint. According to this principle, the natural frequencies of the discrete system without and with the constraint are alternately located along the positive real axis. Although it is commonly believed that the same rule also applied for distributed vibrating systems, no proof has been given for the distributed gyroscopic system. This paper presents several eigenvalue inclusion principles for a class of distributed gyroscopic systems under pointwise constraints. A transfer function formulation is proposed to describe the constrained system. Five types of nondissipative constraints and their effects on the system natural frequencies are studied. It is shown that the transfer function formulation is a systematic and convenient way to handle constraint problems for the distributed gyroscopic system.

Eigenvalue Inclusion Principles for Distributed Gyroscopic Systems

1991 ◽  
Author(s):  
B. Yang
Keyword(s):  
Transfer Function ◽  
Natural Frequencies ◽  
Gyroscopic System ◽  
Constrained System ◽  
Function Formulation ◽  
Pointwise Constraints ◽  
Gyroscopic Systems

Abstract This paper presents several eigenvalue inclusion principles for a class of distributed gyroscopic systems under pointwise constraints. A transfer function formulation is proposed to describe the constrained system. Five types of non-dissipative constraints and their effects on the system natural frequencies are studied It is shown that the natural frequencies of the constrained gyroscopic system alternate with those of the unconstrained system.

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

Stochastic Stability of Gyroscopic Systems Under Bounded Noise Excitation

2018 ◽  
Vol 18 (02) ◽  
pp. 1850022 ◽  
Author(s):  
Jian Deng
Keyword(s):  
Lyapunov Exponent ◽  
Parametric Resonance ◽  
Stochastic Stability ◽  
Largest Lyapunov Exponent ◽  
Gyroscopic System ◽  
Bounded Noise ◽  
Rotating Shaft ◽  
Dynamic Stochastic ◽  
The Largest Lyapunov Exponent ◽  
Gyroscopic Systems

Dynamic stochastic stability of a two-degree-of-freedom gyroscopic system under bounded noise parametric excitation is studied in this paper through moment Lyapunov exponent and the largest Lyapunov exponent. A rotating shaft subject to stochastically fluctuating thrust is taken as a typical example. To obtain these two exponents, the gyroscopic differential equation of motion is first decoupled into Itô stochastic differential equations by using the method of stochastic averaging. Then mathematical transformations are used in these Itô equation to obtain a partial differential eigenvalue problem governing moment Lyapunov exponents, the slope of which at the origin is equal to the largest Lyapunov exponent. Depending upon the numerical relationship between the natural frequency and the excitation frequencies, the gyroscopic system may fall into four types of parametric resonance, i.e. no resonance, subharmonic resonance, combination additive resonance, and combination differential resonance. The effects of noise and frequency detuning parameters on the parametric resonance are investigated. The results pave the way to utilize or control the vibration of gyroscopic systems under stochastic excitation.

Vibration Characteristics of Bladed Disc Assemblies

1973 ◽  
Vol 15 (3) ◽  
pp. 165-186 ◽  
Author(s):  
D. J. Ewins
Keyword(s):  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Complex Modes ◽  
Modes Of Vibration ◽  
Excitation Conditions

A study is made to establish the basic vibration characteristics of bladed disc assemblies. An analysis is presented and used to predict the natural frequencies and mode shapes of uniform bladed discs. It is found that there are many more natural frequencies than those indicated by a study of the blade cantilever modes. The effects of blade detuning are studied and found to give rise to irregular and complex modes of vibration. Consideration of the vibration characteristics under typical operating excitation conditions shows that a detuned system is susceptible to many more resonances than is an equivalent tuned system.

Free vibration analysis of rotating tapered Timoshenko beams via variational iteration method

2016 ◽  
Vol 23 (2) ◽  
pp. 220-234 ◽  
Author(s):  
Yanfei Chen ◽  
Juan Zhang ◽  
Hong Zhang
Keyword(s):  
Free Vibration ◽  
Iteration Method ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Accurate Determination ◽  
Variational Iteration Method ◽  
Mode Shapes ◽  
Engineering Practice ◽  
Timoshenko Beams ◽  
Variational Iteration

Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tapered Timoshenko beams using the technique of variational iteration, which is relatively new and is capable of providing accurate solutions for eigenvalue problems in a quite easy way. Natural frequencies and mode shapes for rotating tapered Timoshenko beams with linearly varying height as well as linearly varying height and width are investigated via two numerical examples, and solutions are compared with results published in literature where available. Since the method constitutes a numerical procedure, the convergence of solutions which is important for practical implementation is evaluated as well, where efficiency and accuracy of variational iteration method in solving high order eigenvalue problems are demonstrated.

Dynamic Characteristics of a Rotating Tapered Cantilevered Timoshenko Beam with Preset and Pre-Twist Angles

2019 ◽  
Vol 19 (04) ◽  
pp. 1950043 ◽  
Author(s):  
Xiangying Guo ◽  
Xiao-Dong Yang ◽  
Shao-Wen Wang
Keyword(s):  
Time Series ◽  
Power Series ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Neutral Line ◽  
Series Method ◽  
Power Series Method ◽  
Complex Modes ◽  
Gyroscopic Coupling ◽  
Rotating Tapered Timoshenko Beam

This paper is concerned with the free vibration of a rotating tapered Timoshenko beam with preset and pre-twist angles. The power series method is used to obtain the frequencies and complex modes of the structure. The rotating velocity related terms are re-classified into three types, namely, static centrifugal terms, dynamic centrifugal terms and the gyroscopic terms. This reclassification provides clearer descriptions of the varying frequencies with respect to the rotating velocity. The gyroscopic coupling among different directions are discussed. The overall contour of the complex modal vibrations is recorded and investigated by time series snapshots of neutral line motions and tip end cross-section motions.

Eigen Solutions of Grouped Turbo Blades Solved by the Generalized Differential Quadrature Method

2001 ◽  
Author(s):  
J. H. Kuang ◽  
M. H. Hsu
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Discrete Eigenvalue ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential ◽  
Eigen Solutions

The eigenvalue problems of grouped turbo blades were numerically formulated by using the generalized differential quadrature method (GDQM). Different boundary approaches accompanying the GDQM to transform the partial differential equations of grouped turbo blades into a discrete eigenvalue problem are discussed. Effects of the number of sample points and the different boundary approaches on the accuracy of the calculated natural frequencies are also studied. Numerical results demonstrated the validity and the efficiency of the GDQM in treating this type of problem.

Eigensolutions of Grouped Turbo Blades Solved by the Generalized Differential Quadrature Method

2002 ◽  
Vol 124 (4) ◽  
pp. 1011-1017 ◽  
Author(s):  
J. H. Kuang ◽  
M. H. Hsu
Keyword(s):  
Partial Differential Equations ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Discrete Eigenvalue ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

The eigenvalue problems of grouped turbo blades were numerically formulated by using the generalized differential quadrature method (GDQM). Different boundary approaches accompanying the GDQM to transform the partial differential equations of grouped turbo blades into a discrete eigenvalue problem are discussed. Effects of the number of sample points and the different boundary approaches on the accuracy of the calculated natural frequencies are also studied. Numerical results demonstrated the validity and the efficiency of the GDQM in treating this type of problem.

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