Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

Hayes, Richard; Marques, Simão

doi:10.1016/j.compstruc.2014.10.010

Cited by 16 publications

(22 citation statements)

References 38 publications

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“…Matrix A reconstructs the Fourier series from the harmonic balance and is shown in the work of Hayes and Marques (9) . The non-linear term Fourier coefficients,Q nl are computed using Discrete Fourier Transforms (DFT).…”

Section: Hdhbmentioning

confidence: 99%

“…Expressions for the transformation matrix E and its inverse E −1 , which can be used to relate the time domain variables back to the Fourier coefficients, i.e.Q = E −1Q , are shown in the work of Hayes and Marques (9) . Using these transformation matrices, Equation (9) can be cast July 2017 The Aeronautical Journal in the time domain as:…”

Section: Hdhbmentioning

confidence: 99%

“…Limit-Cycle Oscillations (LCOs) are also a pertinent issue for some in-service aircraft due to their non-linear nature; hence, they carry considerable practical interest (4,5) . As for flutter, LCOs are sensitive to parametric variability and have been investigated using various uncertainty propagation techniques (6)(7)(8)(9) . Despite the many studies conducted to examine the consequences of parametric uncertainty, there have been few attempts to characterise this uncertainty for aeroelastic problems.…”

Section: Introductionmentioning

confidence: 99%

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Reducing parametric uncertainty in limit-cycle oscillation computational models

2017

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The assimilation of discrete data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters, which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance (HDHB) method. The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on a pitch/plunge aerofoil and two Goland wing configurations. In all cases, significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their true deterministic values. Additionally, a comparison of two approaches to extract the true values from the posterior distributions is presented.

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Section: Hdhbmentioning

confidence: 99%

Section: Hdhbmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reducing parametric uncertainty in limit-cycle oscillation computational models

2017

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“…Moreover, Cameron and Griffin [26] develop an alternate frequency time domain method (AFT) which allows computation of the nonlinear friction forces in the time domain while solving the equations of motion (EQM) in the frequency domain. The EQM are formulated in the frequency domain using the classical harmonic balance method (HBM) [15,27,28] and the recently more popular approach known as multiharmonic balance method (MHBM) [5,8,29], owing to their high computation efficiency compared to the time integration procedure. In conclusion, the AFT method combines the frequency domain EQM with friction forces computed in the time domain at discrete time steps, allowing to capture complex nonlinearities exhibited by the friction forces and other nonlinear behavior while keeping the computational advantage of frequency domain modelling.…”

Section: Introductionmentioning

confidence: 99%

An analytical calculation of the Jacobian matrix for 3D friction contact model applied to turbine blade shroud contact

Afzal

Arteaga

Kari

2016

Computers & Structures

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An analytical expression is formulated to compute the Jacobian matrix for 3D friction contact modelling that efficiently evaluates the matrix while computing the friction contact forces in the time domain by means of the alternate frequency time domain approach. The developed expression is successfully used for the calculation of the friction damping on a turbine blade with shroud contact interface having an arbitrary 3D relative displacement. The analytical expression drastically reduces the computation time of the Jacobian matrix with respect to the classical finite difference method, with many points at the contact interface. Therefore, it also significantly reduces the overall computation time for the solution of the equations of motion, since the formulation of the Jacobian matrix is the most time consuming step in solving the large set of nonlinear algebraic equations when a finite difference approach is employed. The equations of motion are formulated in the frequency domain using the multiharmonic balance method to accurately capture the nonlinear contact forces and displacements. Moreover, the equations of motion of the full turbine blade model are reduced to a single sector model by exploiting the concept of cyclic symmetry boundary condition for a periodic structure. Implementation of the developed scheme in solving the equations of motion is proved to be effective and significant reduction in time is achieved without loss of accuracy.

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“…Since only the periodic motion is captured and the transient part is avoided, it provides significant time cost reduction. The HB method has been proved to be efficient and accurate tool for periodic fluid system, such as LCO prediction (Yao and Marques, 2015;Kivanc and Hall, 2011;Thomas et al, 2002), structural uncertainty analysis (Hayes and Marques, 2015). Through the replacement of the time derivative with the frequency of the unsteady disturbance, the HB technique can be exploited for many unsteady flows in engineering applications, which are inherently periodic in time.…”

Section: Introductionmentioning

confidence: 99%