A Practical Approach for Evaluation of Equivalent Linear Damping From Measurements of Mistuned and/or Non-Linear Stages and Forced Response Validation

2016 ◽  
Author(s):  
Andreas Hartung ◽  
Hans-Peter Hackenberg
Keyword(s):  
Linear Systems ◽  
Forced Response ◽  
Practical Approach ◽  
Response Analysis ◽  
Worst Case ◽  
Equivalent Linear ◽  
Non Linear ◽  
Linear Damping ◽  
Non Linear Systems

The equivalent linear damping is an important parameter for the design of blades and vanes. This parameter will normally be used based on experience and worst case considerations. In this paper, a practical approach for the evaluation of the equivalent linear damping of blade and vane stages from measurements is proposed. The method can especially be used for mistuned and/or non-linear systems as well as in case of non-satisfying quality of the measurement signals. Based on the approach developed, a way for the validation of the forced response analysis is presented.

Non-linear disturbance observer-based adaptive composite anti-disturbance control for non-linear systems with dynamic non-harmonic multisource disturbances

2017 ◽  
Vol 40 (12) ◽  
pp. 3458-3465 ◽  
Author(s):  
Zheng Wang ◽  
Jianping Yuan
Keyword(s):  
Linear Systems ◽  
Disturbance Observer ◽  
Control Structure ◽  
Non Linear ◽  
Linear Damping ◽  
Non Linear Systems ◽  
Complex Features ◽  
The Stability ◽  
Linear Disturbance ◽  
Adaptive Composite

In this paper, an adaptive composite anti-disturbance control structure is constructed for a class of non-linear systems with dynamic non-harmonic multisource disturbances. The key point of this paper is that a kind of non-harmonic disturbance, which has non-linear internal dynamics and complex features, is involved. A non-linear exogenous system is employed to describe the dynamic non-harmonic disturbances and several useful assumptions are introduced. By introducing a non-linear damping term, a novel adaptive non-linear disturbance observer is constructed. Based on the disturbance/uncertainty estimation and attenuation (DUEA) schemes, a composite anti-disturbance control structure is synthesized. Meanwhile, a new sufficient condition is derived and the stability of the closed-loop system is proved. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.

A Harmonic Analysis for the Steady Analysis of Non-Linear Systems

2012 ◽  
Vol 433-440 ◽  
pp. 5536-5541
Author(s):  
Shan Chai ◽  
Can Chang Liu ◽  
Hong Yan Li
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Steady State Solution ◽  
Response Analysis ◽  
Time Interval ◽  
Harmonic Response ◽  
Non Linear ◽  
Non Linear Systems ◽  
Harmonic Response Analysis ◽  
Linear Differential

A numerical analysis is used to investigate the response of non-linear systems under aperiodic excitations based on the harmonic response analysis method. An idea of fine discretization is proposed to turn the aperiodic excitations into the superposition of a series of periodic excitations in a tiny time interval. The method of perturbation is employed to transform the non-linear governing equation into a series of linear differential equations. Harmonic response analysis can be applied in the solution of aperiodic steady response. The algebraic algorithm of direct steady-state analysis can improve computational efficiency. The defect that the steady-state solution can be gotten out until the free vibration attenuates is avoided. The examples show that the numerical results match well with the analytic data.

Neural Element Harmonic Response Analysis for the Aperiodic Steady Response of Non-Linear Systems

2012 ◽  
Vol 433-440 ◽  
pp. 871-875
Author(s):  
Can Chang Liu ◽  
Shan Chai ◽  
Lu Liu ◽  
Hong Yan Li
Keyword(s):  
Linear Systems ◽  
Response Analysis ◽  
Neural Element ◽  
Analysis Method ◽  
Element Discretization ◽  
Harmonic Response ◽  
Non Linear ◽  
Non Linear Systems ◽  
Harmonic Response Analysis ◽  
Linear Differential

A novel numerical analysis was used to investigate the response of non-linear systems undergoing aperiodic excitations based on the Neural Harmonic Response Analysis method (NNHRAM). A numerical method of neural element discretization was proposed to turn the aperiodic excitations into superposition of a series of periodic excitations. The method of perturbation was applied to transform the non-linear governing equation into a series of linear differential equations. The method of NNHRAM could be used to solve the aperiodic steady response. The algebraic algorithm of direct steady-state analysis can improve the computational efficiency. The examples showed that the numerical results match well with the analytic solution.

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

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