Piecewise constrained optimization harmonic balance method for predicting the limit cycle oscillations of an airfoil with various nonlinear structures

Liao, Hua

doi:10.1016/j.jfluidstructs.2015.03.008

Cited by 12 publications

(3 citation statements)

References 21 publications

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“…In [14], the sensitivity analysis is extended to fractional-order nonlinear system with delay as nonlinear fractional delay differential equations are a very recent topic. Recently, the sensitivities of an airfoil system with various nonlinear structures are studied in [15].…”

Section: Introductionmentioning

confidence: 99%

Efficient sensitivity analysis method for chaotic dynamical systems

Liao

2016

Journal of Computational Physics

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The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.

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Section: Introductionmentioning

confidence: 99%

Efficient sensitivity analysis method for chaotic dynamical systems

Liao

2016

Journal of Computational Physics

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“…Any changes in the parameters from the established baseline dynamics of the system are leveraged to identify potential damage or failures [16,17]. The estimated dynamic parameters from an output signal can be utilized for detecting instabilities [18], faults [19], or disturbances in the system components [20], and subsequently for estimating their impact on the overall performance [21,22].…”

Section: Introductionmentioning

confidence: 99%

Highly Sensitive Nonlinear Identification to Track Early Fatigue Signs in Flexible Structures

Habtour

Maio

Masmeijer

et al. 2021

Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems

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This study describes a physics-based and data-driven nonlinear system identification approach for detecting early fatigue damage due to vibratory loads. The approach also allows for tracking the evolution of damage in real-time. Nonlinear parameters such as geometric stiffness, cubic damping and phase angle shift can be estimated as a function of fatigue cycles, which are demonstrated experimentally using flexible aluminum 7075-T6 structures exposed to vibration. Nonlinear system identification is utilized to create and update nonlinear frequency response functions, backbone curves and phase traces to visualize and estimate the structural health. Findings show that the dynamic phase is more sensitive to the evolution of early fatigue damage than nonlinear parameters such as the geometric stiffness and cubic damping parameters. A modifed Carrella-Ewins method is introduced to calculate the backbone from the nonlinear signal response, which is in good agreement with the numerical and harmonic balance results. The phase tracing method is presented, which appears to detect damage after approximately 40% of fatigue life, while the geometric stiffness and cubic damping parameters are capable of detecting fatigue damage after approximately 50% of the life-cycle.

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“…Piecewise nonlinear functions are also used to analyze aeroelastic systems with complex piecewise nonlinear structural stiffness [30,31]. Sun et al [32] approximated the static lift coefficient by a fourth-order piecewise polynomial function.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber

Lelkes

Kalmár‐Nagy

2020

Nonlinear Dyn

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The dynamics of a two-degrees-of-freedom (pitch–plunge) aeroelastic system is investigated. The aerodynamic force is modeled as a piecewise linear function of the effective angle of attack. Conditions for admissible (existing) and virtual equilibria are determined. The stability and bifurcations of equilibria are analyzed. We find saddle-node, border collision and rapid bifurcations. The analysis shows that the pitch–plunge model with a simple piecewise linear approximation of the aerodynamic force can reproduce the transition from divergence to the complex aeroelastic phenomenon of stall flutter. A linear tuned vibration absorber is applied to increase stall flutter wind speed and eliminate limit cycle oscillations. The effect of the absorber parameters on the stability of equilibria is investigated using the Liénard–Chipart criterion. We find that with the vibration absorber the onset of the rapid bifurcation can be shifted to higher wind speed or the oscillations can be eliminated altogether.

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Piecewise constrained optimization harmonic balance method for predicting the limit cycle oscillations of an airfoil with various nonlinear structures

Cited by 12 publications

References 21 publications

Efficient sensitivity analysis method for chaotic dynamical systems

Efficient sensitivity analysis method for chaotic dynamical systems

Highly Sensitive Nonlinear Identification to Track Early Fatigue Signs in Flexible Structures

Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber

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