• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.12
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• pp.1153-1161
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• 2010

An efficient solution method for harmonic balance techniques with Fourier transform is presented for periodic unsteady flow problems. The present partially-implicit harmonic balance treats the flux terms implicitly and the harmonic source term is solved explicitly. The convergence of the partially Implicit method is much faster than the explicit Runge-Kutta harmonic balance method. The method does not need to compute the additional flux Jacobian matrix from the implicit harmonic source term. Compared with fully implicit harmonic balance method, this partial approach turns out to have good convergence property. Oscillating flows over NACA0012 airfoil are considered to verify the method and to compare with results of explicit R-K(Runge-Kutta) and dual time stepping methods.

• Journal of computational fluids engineering
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• v.15 no.4
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• pp.76-84
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• 2010

In order to analyze the periodic unsteady flow problem efficiently the partially implicit harmonic balance (PIHB) method was developed. Contrary to the existing harmonic balance method, this method handles the harmonic source term explicitly and deals with flux terms implicitly. This method has a good convergence in comparison with the full explicit harmonic method and it is easy to apply this method because there is no need to calculate the complicated flux Jacobian term by comparing with the full implicit harmonic method. With the multigrid method about the each harmonic it turns out that this method has a good convergence regardless of the number of harmonics. The oscillating flows over NACA0012 airfoil is considered to verify this method then the result correponsed to both the result of dual time stepping and explicit Runge-Kutta method.

• Journal of KSNVE
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• v.8 no.5
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• pp.887-899
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• 1998

It has been resulted that Lagrange multiplier method with statistical approach was superior to traditional harmonic balance method in identifying the nonlinear loudspeaker parameters when output signals were contaminated with Gaussian random noise. We have known that the displacement-dependent characteristic values of nonlinear parameters identified by traditional harmonic balance method were estimated less than original values by the increase of output noise and the stiffness coefficients were very sensitive to output noise. Also, by the sensitivity analysis we have verified that the harmonic distortions in acoustic radiation was mainly due to nonlinearity of force factor caused by uneven magnetic fields and that reducing the nonlinearity of damping coefficients were very effective for improving second harmonic distrotion of acoustic radiation.

• Journal of Mechanical Science and Technology
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• v.15 no.11
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• pp.1507-1516
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• 2001

An analytical method is presented for evaluation of the steady state periodic behavior of nonlinear structural systems. This method is based on the substructure synthesis formulation and a harmonic balance procedure, which is applied to the analysis of nonlinear responses. A complex nonlinear system is divided into substructures, of which equations are approximately transformed to modal coordinates including nonlinear term under the reasonable procedure. Then, the equations are synthesized into the overall system and the nonlinear solution for the system is obtained. Based on the harmonic balance method, the proposed procedure reduces the size of large degrees-of-freedom problem in the solving nonlinear equations. Feasibility and advantages of the proposed method are illustrated using the study of the nonlinear rotating machine system as a large mechanical structure system. Results obtained are reported to be an efficient approach with respect to nonlinear response prediction when compared with other conventional methods.

• Journal of Power Electronics
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• v.18 no.6
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• pp.1659-1669
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• 2018

An improved circulating current suppression control method is proposed in this paper. In the proposed controller, an outer loop of the average capacitor voltage control model is used to balance the sub-module capacitor voltage. Meanwhile, an individual voltage balance controller and an arm voltage balance controller are also used. The DC and harmonic components of the circulating current are separated using a low pass filter. Therefore, a multiple quasi-proportional-resonant (multi-quasi-PR) controller is introduced in the inner loop to eliminate the circulating harmonic current, which mainly contains second-order harmonic but also contains other high-order harmonics. In addition, the parameters of the multi-quasi-PR controller are designed in the discrete domain and an analysis of the stability characteristic is given in this paper. In addition, a simulation model of a three-phase MMC system is built in order to confirm the correctness and superiority of the proposed controller. Finally, experiment results are presented and compared. These results illustrate that the improved control method has good performance in suppressing circulating harmonic current and in balancing the capacitor voltage.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.17 no.6
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• pp.124-129
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• 2018

A non-linear vibration isolation system which is composed of a non-linear spring and a linear damper was proposed in past research. When the support of the isolation system is excited harmonically, the response component of the isolation system mass at the excitation frequency has been calculated approximately using the harmonic balance method. The response was approximated by a single mode, and the result was compared with a numerical result which is assumed as an accurate one. Next, the response was approximated by two modes, and the result was compared with the former one.

• Journal of Electrical Engineering and Technology
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• v.6 no.5
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• pp.697-705
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• 2011

In this paper, a closed-loop system constructed with a linear plant and nonlinearity in the feedback connection is considered to argue against its planar orbital stability. Through a state space approach, a main result that presents a sufficient stability criterion of the limit cycle predicted by solving the harmonic balance equation is given. Preliminarily, the harmonic balance of the nonlinear feedback loop is assumed to have a solution that determines the characteristics of the limit cycle. Using a state-space approach, the nonlinear loop equation is reformulated into a linear perturbed model through the introduction of a residual operator. By considering a series of transformations, such as a modified eigenstructure decomposition, periodic averaging, change of variables, and coordinate transformation, the stability of the limit cycle can be simply tested via a scalar function and matrix. Finally, the stability criterion is addressed by constructing a composite Lyapunov function of the transformed system.

• Journal of computational fluids engineering
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• v.16 no.4
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• pp.21-27
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• 2011

In this paper, the diagonal implicit harmonic balance method is applied to analyze helicopter rotor blade flow. The periodic boundary condition for Fourier coefficients is also applied in hover and forward flight conditions. It is available enough to simulate the forward flight problem with only one rotor blade using the periodic boundary condition in the frequency domain. In order to demonstrate the present method, Caradonna & Tung's rotor blades were used and the results were compared to the time-accurate method and experimental data.

• Journal of computational fluids engineering
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• v.17 no.1
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• pp.70-77
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• 2012

In this paper, diagonal implicit harmonic balance method with overset grid technique is applied to analyze helicopter rotor blade flow in hover and forward flight condition. The chimera grid need interpolation time with sub-grid and background grid in moving problem such as forward flight on every time step. Present method is available enough to reduce the grid module interpolation time. In order to demonstrate present method, Caradonna & Tung's and AH-1G rotor blades are used and the results are compared to other researchers' result and experimental data.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.543-549
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• 2011

In this paper, diagonal implicit harmonic balance method is applied to analyze helicopter rotor blade flow. Periodic boundary condition for Fourier coefficients is also applied in hover and forward flight condition. It is available enough to simulate the forward flight problem with only one rotor blade using the periodic boundary condition in frequency domain. In order to demonstrate present method Carodonna & Tung's rotor blades are used and the results are compared to time-accurate method and experimental data.