Relevant bibliographies by topics / Harmonic balance methods

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Harmonic balance methods'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Harmonic balance methods"

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Handy, C. R. "Combining the methods of harmonic balance and Kryloff-Bogoliuboff." Journal of Sound and Vibration 102, no. 2 (1985): 243–46. http://dx.doi.org/10.1016/s0022-460x(85)80056-0.

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Hall, Kenneth C., Kivanc Ekici, Jeffrey P. Thomas, and Earl H. Dowell. "Harmonic balance methods applied to computational fluid dynamics problems." International Journal of Computational Fluid Dynamics 27, no. 2 (2013): 52–67. http://dx.doi.org/10.1080/10618562.2012.742512.

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ROBBIO, FEDERICO I., DIEGO M. ALONSO, and JORGE L. MOIOLA. "DETECTION OF LIMIT CYCLE BIFURCATIONS USING HARMONIC BALANCE METHODS." International Journal of Bifurcation and Chaos 14, no. 10 (2004): 3647–54. http://dx.doi.org/10.1142/s0218127404011491.

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In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy matrix. Period-doubling, pitchfork and Neimark–Sacker bifurcations of cycles are detected close to a Gavrilov–Guckenheimer singularity in two modified Rössler systems. This special singularity has a zero eigenvalue and a pair of pure imaginary eigenvalues in the linearization of the flow around its equilibrium. The presented results suggest that the proposed technique can be promising in analyzing limit cycle bifurcations arising in the unfoldings of other complex singularities.
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Pierre, C., A. A. Ferri, and E. H. Dowell. "Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method." Journal of Applied Mechanics 52, no. 4 (1985): 958–64. http://dx.doi.org/10.1115/1.3169175.

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A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.
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Handy, C. R. "Harmonic balance methods and the theory of generalized Padé approximants." Journal of Sound and Vibration 102, no. 2 (1985): 247–57. http://dx.doi.org/10.1016/s0022-460x(85)80057-2.

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Wei Dong and Peng Li. "Hierarchical Harmonic-Balance Methods for Frequency-Domain Analog-Circuit Analysis." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 26, no. 12 (2007): 2089–101. http://dx.doi.org/10.1109/tcad.2007.907018.

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Hiamang, S., and R. E. Mickens. "Harmonic Balance: Comparison of Equation of Motion and Energy Methods." Journal of Sound and Vibration 164, no. 1 (1993): 179–81. http://dx.doi.org/10.1006/jsvi.1993.1204.

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YTTERDAL, TROND, TOR A. FJELDLY, and MICHAEL S. SHUR. "BEYOND SPICE, A REVIEW OF MODERN ANALOG CIRCUIT SIMULATION TECHNIQUES." International Journal of High Speed Electronics and Systems 09, no. 03 (1998): 783–805. http://dx.doi.org/10.1142/s0129156498000324.

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We present a review of modern analog simulation techniques based on time- and frequency-domain algorithms. For time-domain techniques, important topics such as circuit decomposition, relaxation methods, latency, multirate integration, continuation methods, parallel algorithms, and finite difference time-domain methods are discussed. Frequency-domain simulation techniques included are harmonic balance, harmonic relaxation, harmonic-Newton, spectral balance, methods for quasiperiodic circuits, and device modeling for frequency domain simulators. Also included are examples of modern simulators.
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Gorgadze, Svetlana F., and Anton A. Maximov. "HARMONIC BALANCE THEORY FOR SCHEME TECHNICAL DESIGN." T-Comm 14, no. 11 (2020): 21–32. http://dx.doi.org/10.36724/2072-8735-2020-14-11-21-32.

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The analysis and generalization of the main publications on the methods of synthesis and analysis of non-linear active microwave circuits based on the use of the harmonic balance method are presented. As a result of some classification of mathematical approaches and techniques used in the context of this method, a selection and review of basic algorithms was made, the sequential application of which makes it possible to obtain the final result for a scheme of any complexity. The principles of drawing up the initial system of differential equations for electronic circuits and reducing it to a system of linear algebraic equations are considered. A detailed and, at the same time, simplified interpretation of the approaches involving the use of projection methods and Krylov subspaces is given in order to make them easier to understand. Both the complete and the restart generalized method of minimal residuals are considered, in which the desired solution is obtained in the course of an iterative process, at each stage of which subspaces of lower dimension are constructed. The possibilities of simulators and application packages intended for circuit design of electronic circuits are considered. The problem of matching a power amplifier in large signal mode using the APLAC simulator, which is NI AWR technology for designing high-frequency circuits, is discussed.
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Attar, Peter J. "Using Pseudotime Solution Framework in Harmonic Balance Methods for Aperiodic Problems." AIAA Journal 51, no. 12 (2013): 2982–87. http://dx.doi.org/10.2514/1.j052635.

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Dissertations / Theses on the topic "Harmonic balance methods"

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Magnevall, Martin. "Methods for Simulation and Characterization of Nonlinear Mechanical Structures." Licentiate thesis, Karlskrona : Blekinge Institute of Technology, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-00430.

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Trial and error and the use of highly time-consuming methods are often necessary for modeling, simulating and characterizing nonlinear dynamical systems. However, for the rather common special case when a nonlinear system has linear relations between many of its degrees of freedom there are particularly interesting opportunities for more efficient approaches. The aim of this thesis is to develop and validate new efficient methods for the theoretical and experimental study of mechanical systems that include significant zero-memory or hysteretic nonlinearities related to only small parts of the whole system. The basic idea is to take advantage of the fact that most of the system is linear and to use much of the linear theories behind forced response simulations. This is made possible by modeling the nonlinearities as external forces acting on the underlying linear system. The result is very fast simulation routines where the model is based on the residues and poles of the underlying linear system. These residues and poles can be obtained analytically, from finite element models or from experimental measurements, making these forced response routines very versatile. Using this approach, a complete nonlinear model contains both linear and nonlinear parts. Thus, it is also important to have robust and accurate methods for estimating both the linear and nonlinear system parameters from experimental data. The results of this work include robust and user-friendly routines based on sinusoidal and random noise excitation signals for characterization and description of nonlinearities from experimental measurements. These routines are used to create models of the studied systems. When combined with efficient simulation routines, complete tools are created which are both versatile and computationally inexpensive. The developed methods have been tested both by simulations and with experimental test rigs with promising results. This indicates that they are useful in practice and can provide a basis for future research and development of methods capable of handling more complex nonlinear systems.
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Peterson, Marshall Warren. "Implementations of Fourier Methods in CFD to Analyze Distortion Transfer and Generation Through a Transonic Fan." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/6384.

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Inlet flow distortion is a non-uniform total pressure, total temperature, or swirl (flow angularity) condition at an aircraft engine inlet. Inlet distortion is a critical consideration in modern fan and compressor design. This is especially true as the industry continues to increase the efficiency and operating range of air breathing gas turbine engines. The focus of this paper is to evaluate the Computational Fluid Dynamics (CFD) Harmonic Balance (HB) solver in STAR-CCM+ as a reduced order method for capturing inlet distortion as well as the associated distortion transfer and generation. New methods for quantitatively describing and analyzing distortion transfer and generation are investigated. The geometry used is the rotor 4 fan geometry, consisting of one rotor and one stator. The inlet boundary condition is a 90-degree sector total pressure distortion profile with total pressure and swirl held constant. Multiple HB simulations with varying mode combinations and distortion intensities are analyzed and compared against full annulus Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. Best practices and recommendations for the implementation of the HB solver are given. The pre-existing Society of Automotive Engineers Aerospace Recommended Practice (SAE-ARP) 1420b descriptors are demonstrated to be inadequate for the purposes of analyzing distortion transfer and generation on a stage-to-stage basis. New implementations of Fourier methods are presented as an alternative to the SAE-ARP 1420b descriptors. These Fourier descriptors are shown to describe distortion transfer and generation to a higher degree of fidelity than the SAE-ARP 1420b descriptors. These new descriptors are demonstrated on the analysis of full annulus URANS and HB simulations. The HB solver is shown to be capable of capturing distortion transfer, generation and performance degradation. Recommendations for the optimal implementation of the HB method are given.
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Erbay, Ali. "Parameter Study of Ferro-Resonance with Harmonic Balance Method." Thesis, KTH, Elektriska energisystem, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-102090.

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Ferro‐resonance is an electrical phenomenon which can cause damage to electrical equipments of power systems by its characteristic steady state over voltages and over currents. Configurations where ferro‐resonance is possible has more than one steady state operation. With time domain simulations, different dangerous steady state operations are hard to find due to the fact of dependancy of initial conditions and parameters of the system. Determination of risk of ferro‐resonance needs special studies involving frequency domain and Fourier series based harmonic balance method. Two different types of harmonic balance method are used; namely analytical and numerical method. In order to draw twoparameter continuous curves, harmonic balance with hyper‐sphere continuation method algorithm is created in MATHCAD environment. Work of two case studies in academic literature are extended by comparing different system parameter curves and calculating stability domain risk zones for fundamental ferro‐resonance, subharmonic‐1/2 and subharmonic ‐1/3 ferro‐resonance. Alstom’s test system is also investigated with approximations. Application of numerical harmonic balance method is more superior than analytical method since it is ease of use with thevenin equivalents rather than deriving system equation by hand and possibility to study subharmonic ferro‐resonance. Hypersphere continuation method worked well enough to turn limit points on parameter curves depending on considered Fourier components. Critical values for system parameters have been found for each type of ferro‐resonance allowing to analyse normal operation and ferroresonance operation regimes. Critical values of static damping resistor in the system can be calculated by harmonic balance method without using empirical formula. Damping resistor calculated by harmonic balance method showed difference than the one calculated by empirical formula. Fundamental and subharmonic ferro‐resonance solutions existence zones are co‐existant and sensitive to parameter changes therefore same attention should be given to subharmonic as in fundamental ferro‐resonance. For future studies, three‐phase models for harmonic balance method should be developed in order to study neutral isolated networks and a more customized method of solving non‐linear harmonic balance equations for faster computation can also be developed in MATLAB environment.
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Wong, Wai Kuen. "Simulation of nonlinear microwave circuits using harmonic balance method." Ohio : Ohio University, 1988. http://www.ohiolink.edu/etd/view.cgi?ohiou1182874498.

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Knapke, Robert. "High-Order Unsteady Heat Transfer with the Harmonic Balance Method." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1427962937.

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Moulin, Johann. "On the flutter bifurcation in laminar flows : linear and nonlinear modal methods." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX093.

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L'instabilité de flottement a été le sujet de nombreuses études depuis le milieu du vingtième siècle à cause de ses applications critiques en aéronautique. Elle est classiquement décrite comme un instabilité linéaire en écoulement potentiel, mais les effets visqueux et nonlinéaires du fluide peuvent avoir un impact crucial.La première partie de cette thèse est consacrée au développement de méthodes théoriques et numériques pour l'analyse linéaire et nonlinéaire de la dynamique d'une ``section typique aéroélastique'' --- une plaque montée sur des ressorts de flexion et torsion --- plongée dans un écoulement laminaire bidimensionnel modélisé par les équations de Navier--Stokes incompressibles.D'abord, on développe une analyse faiblement nonlinéaire pour étudier le régime basse amplitude, puis, une approche d'équilibrage harmonique, connue comme la Méthode Spectrale en Temps (TSM), de façon à capturer des solutions de flottement plus fortement nonlinéaires. Le défi de la résolution numérique des équations TSM est relevé grâce au développement d'une approche parallèle en temps de type Newton--Krylov, combinée à un préconditionneur spécialement développé, dit ``bloc-circulant''.La seconde partie de la thèse est dédiée à l'étude physique de la bifurcation de flottement. On commence par revisiter le problème de stabilité linéaire en mettant en lumière, en particulier, les effets de viscosité.On poursuit avec l'étude des effets nonlinéaires fluides: les structures légères et les hauts nombres de Reynolds favorisent des bifurcations sous-critiques.On achève cette partie en étudiant l'apparition de modulations de basse fréquence sur des solutions périodiques de flottement. On explique ce comportement par une instabilité linéaire (Floquet) de cycle limite.La dernière partie de la thèse vise à initier l'extension des différentes méthodes évoquées précédemment pour le cas de configurations tridimensionnelles à grande échelle. En guise de premier pas vers cet objectif à long terme, on développe un outil open-source massivement parallèle capable de réaliser l'analyse de stabilité linéaire hydrodynamique (structure figée) d'écoulements tridimensionnels possédant plusieurs dizaines de millions de degrés de liberté<br>The flutter instability has been the focus of numerous works since the middle of the twentieth century, due to its critical application in aeronautics. Flutter is classically described as a linear instability using potential flow models, but viscous and nonlinear fluid effects may both crucially impact this aeroelastic phenomenon.The first part of this thesis is devoted to the development of theoretical and numerical methods for analyzing the linear and nonlinear dynamics of a ``typical aeroelastic section'' --- a heaving and pitching spring-mounted plate --- immersed in a two-dimensional laminar flow modeled by the incompressible Navier--Stokes equations.First, we develop a semi-analytical weakly nonlinear analysis to efficiently study the small amplitude regime. Second, we develop a harmonic balance-type method, known as the Time Spectral Method (TSM), in order to tackle highly-nonlinear periodic flutter solutions. The challenging task of solving the TSM equations is tackled via a time-parallel Newton--Krylov approach in combination with a new, so-called block-circulant preconditioner.The second part of the thesis focuses on the physical investigation of the flutter bifurcation. We start by revisiting the linear stability problem using a Navier--Stokes fluid model allowing to highlight, in particular, the effect of viscosity.We continue our route on the flutter bifurcation by investigating the effect of fluid nonlinearities: low solid-to-fluid mass ratios and increasing Reynolds numbers foster subcritical bifurcations.We conclude our study by investigating the appearance of low-frequency amplitude modulations on top of a previously established periodic flutter solution. We explain this behavior by a (Floquet) linear instability of periodic solutions.The last part of the thesis aims at initiating the extension of the different methods previously evoked to large-scale three-dimensional configurations. As a first step towards this long-term goal, we develop an open-source massively parallel tool, able to perform hydrodynamic (the structure is fixed) linear stability analysis of three-dimensional flows possessing several tens of millions of degrees of freedom
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GUIDOTTI, EMANUELE. "Analysis of the Unsteady Flow in an Aspirated Counter-Rotating Compressor Using the Nonlinear Harmonic Balance Method." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1218690946.

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Cankaya, Ilyas. "Investigation of jump phenomenon on ship roll motion by generalized harmonic balance method." Thesis, University of Sussex, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263151.

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Nicholson, Robert Kirk. "Computer code for interactive rotorcraft preliminary design using a harmonic balance method for rotor trim /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1993. http://handle.dtic.mil/100.2/ADA274924.

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Thesis (M.S. in Aeronautical Engineering) Naval Postgraduate School, September 1993.<br>Thesis advisor(s): E. Roberts Wood. "September 1993." Includes bibliographical references. Also available online.
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Nicholson, Robert Kirk Jr. "Computer code for interactive rotorcraft preliminary design using a harmonic balance method for rotor trim." Thesis, Monterey, California. Naval Postgraduate School, 1993. http://hdl.handle.net/10945/39985.

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Approved for public release; distribution is unlimited.<br>The Joint Army/Navy Rotorcraft Analysis and Design (JANRAD) computer program was developed to aid in the analysis of helicopter rotor performance, stability and control, and rotor dynamics. JANRAD is an interactive, user friendly program, capable of accurately and quickly solving helicopter design problems at the preliminary design level. The program was written as a collection of MATLAB script and function files (M-files) using the 386-MATLAB version 3.5 programming language. The M-file janrad. in invokes the user interface routines and calls various analysis modules (M-files) which contain the appropriate analysis and output routines. Each of these modules use a common routine, trim.m, which employs blade element theory and a harmonic balance method for rotor trim. The program is limited to conditions of steady flight with no winds and is accurate at a hover and for forward airspeeds greater than or equal to 50 knots.
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Books on the topic "Harmonic balance methods"

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Truly nonlinear oscillations: Harmonic balance, parameter expansions, iteration, and averaging methods. World Scientific, 2010.

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Lu, Junwei, Xiaojun Zhao, and Sotoshi Yamada. Harmonic Balance Finite Element Method. John Wiley & Sons Singapore Pte. Ltd, 2016. http://dx.doi.org/10.1002/9781118975770.

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Adaptive Harmonic Balance Method for Unsteady, Nonlinear, One- Dimensional Periodic Flows. Storming Media, 2002.

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Lu, Junwei, Xiaojun Zhao, and Sotoshi Yamada. Harmonic Balance Finite Element Method: Applications in Nonlinear Electromagnetics and Power Systems. Wiley & Sons, Incorporated, John, 2016.

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Lu, Junwei, Xiaojun Zhao, and Sotoshi Yamada. Harmonic Balance Finite Element Method: Applications in Nonlinear Electromagnetics and Power Systems. Wiley-Interscience, 2016.

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Lu, Junwei, Xiaojun Zhao, and Sotoshi Yamada. Harmonic Balance Finite Element Method: Applications in Nonlinear Electromagnetics and Power Systems. Wiley & Sons, Incorporated, John, 2016.

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Book chapters on the topic "Harmonic balance methods"

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Jazar, Reza N. "Harmonic Balance Method." In Perturbation Methods in Science and Engineering. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73462-6_4.

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Kundert, Kenneth S., Jacob K. White, and Alberto Sangiovanni-Vincentelli. "Harmonic Balance Theory." In Steady-State Methods for Simulating Analog and Microwave Circuits. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-2081-5_5.

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Kundert, Kenneth S., Jacob K. White, and Alberto Sangiovanni-Vincentelli. "Implementing Harmonic Balance." In Steady-State Methods for Simulating Analog and Microwave Circuits. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-2081-5_6.

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Sert, Onur, and Ender Ciğeroğlu. "Adaptive Harmonic Balance Methods, A Comparison." In Special Topics in Structural Dynamics, Volume 6. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29910-5_29.

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Marinca, Vasile, and Nicolae Herisanu. "The Method of Harmonic Balance." In Nonlinear Dynamical Systems in Engineering. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22735-6_3.

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Cvijetić, Gregor, and Hrvoje Jasak. "Harmonic Balance Method for Turbomachinery Applications." In OpenFOAM®. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-60846-4_17.

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De Gersem, H., Stefan Vandewalle, and Kay Hameyer. "Krylov Subspace Methods for Harmonic Balanced Finite Element Methods." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56470-3_39.

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Kudryashova, E. V., N. V. Kuznetsov, O. A. Kuznetsova, G. A. Leonov, and R. N. Mokaev. "Harmonic Balance Method and Stability of Discontinuous Systems." In Dynamics and Control of Advanced Structures and Machines. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-90884-7_11.

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Hu, Qiang, Derong Luo, and Yong Wang. "Harmonic Flux Distribution in Transformer Based on Harmonic-Balance Finite Element Method." In Lecture Notes in Electrical Engineering. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-4981-2_11.

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Zhao, Xiaojun. "Harmonic-Balanced Finite Element Method and Its Application." In Modeling and Application of Electromagnetic and Thermal Field in Electrical Engineering. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0173-9_6.

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Conference papers on the topic "Harmonic balance methods"

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Junge, Laura, Graham Ashcroft, Hans-Peter Kersken, and Christian Frey. "On the Development of Harmonic Balance Methods for Multiple Fundamental Frequencies." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75495.

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Due to the relative motion between adjacent blade rows the aerodynamic flow fields within turbomachinery are usually dominated by deterministic, periodic phenomena. In the numerical simulation of such unsteady flows, (nonlinear) frequency-domain methods are therefore attractive as they are capable of fully exploiting the given spatial and temporal periodicity, as well as modelling flow nonlinearities. A nontrivial issue in the application of frequency-domain methods to turbomachinery flows is to simultaneously capture disturbances with multiple fundamental frequencies in one relative system. In case of harmonically related frequencies, the interval spanned by the sampling points typically resolves the common fundamental frequency. To avoid signal aliasing the highest harmonic of the common frequency should be sampled with an appropriate number of sampling points. However, when the common fundamental frequency is very low in relation to the frequencies of primary interest, equidistant time sampling leads to a high number of sampling points, hence frequency-domain methods can become computationally inefficient. Furthermore, when a problem can no longer be described by harmonic perturbations that are integer multiples of one fundamental frequency, as it may occur in two-shaft configurations, the standard discrete Fourier transform is no longer suitable and the basic harmonic balance method requires extension. In this article two nonlinear frequency-domain approaches for dealing with the accounted issues are demonstrated and compared. The first approach is a generalized harmonic balance method based on almost periodic Fourier transforms with non-equidistant time sampling. Then the so-called harmonic set approach, developed by the authors, is evaluated. Based on the neglection of the nonlinear, quadratic cross-coupling terms between higher harmonics of different fundamental frequencies, the harmonic set approach allows the superposition of periodic disturbances with different fundamental frequencies as well as the separated, equidistant sampling of the highest harmonic of each base frequency. The aim of this paper is to compare the computational efficiency and accuracy of the two methods and assess the impact of neglecting the quadratic cross-coupling terms.
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Kamakoti, Ramji, Liping Xue, Patrick Hu, Peter Attar, and Prakash Vedula. "Harmonic Balance Methodology for Meshless Particle-Based Methods." In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-653.

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Junge, Laura, Christian Frey, Graham Ashcroft, and Edmund Kügeler. "A New Harmonic Balance Approach Using Multidimensional Time." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-16224.

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Abstract Over the past years, nonlinear frequency-domain methods have become a state-of-the-art technique for the numerical simulation of unsteady flow fields within multistage turbomachinery as they are capable of fully exploiting the given spatial and temporal periodicities, as well as modelling flow nonlinearities in a computationally efficient manner. Despite this success, it still remains a significant challenge to capture nonlinear interaction effects within the context of configurations with multiple fundamental frequencies. If all frequencies are integer multiples of a common fundamental frequency, the interval spanned by the sampling points typically resolves the period of the common base frequency. For configurations in which the common frequency is very low in relation to the frequencies of primary interest, many sampling points are required to resolve the highest harmonic of the common fundamental frequency and the method becomes inefficient. In addition when a problem can no longer be described by harmonic perturbations that are integer multiples of one fundamental frequency, as it may occur in two-shaft configurations or when simulating the nonlinear interaction in the context of forced response or flutter, then the standard discrete Fourier transform is no longer suitable and the basic harmonic balance method requires extension. One possible approach is to use almost periodic Fourier transforms with equidistant or non-equidistant time sampling. However, the definition of suitable sampling points that lead to well-conditioned Fourier transform matrices and small aliasing errors is an intricate issue and far from straightforward. To overcome the issues regarding multi-frequency problems described above, a new harmonic balance approach based on multidimensional Fourier transforms in time is presented. The basic idea of the approach is that, instead of defining common sampling points in a common time period, separate time domains, one for each base frequency, are spanned and the sampling points are computed equidistantly within each base frequency’s period. Since the sampling domain is now extended to a multidimensional time-domain, all time instant combinations covering the whole multidimensional domain are computed as the Cartesian product of the sampling points on the axes. In a similar fashion the frequency-domain is extended to a multidimensional frequency-domain by the Cartesian product of the harmonics of each base frequency, so that every point defined by the Cartesian product is an integer linear combination of the occurring frequencies. In this way the proposed method is capable of fully integrating the nonlinear coupling effects between higher harmonics of different fundamental frequencies by using multidimensional discrete Fourier transforms within the harmonic balance solution procedure. The aim of this paper is to introduce the multidimensional harmonic balance method in detail and demonstrate the capability of the approach to simultaneously capture unsteady disturbances with arbitrary excitation frequencies. Therefore the well established aeroelasticity testcase standard configuration 10 in the presence of an artificial inflow disturbance, that mimics an upstream blade wake, is investigated. The crucial aspect of the proposed testcase is that a small ratio of the frequency of the inflow disturbance and the blades vibration frequency is chosen. To demonstrate the advantages of the newly proposed multidimensional harmonic balance approach, the results are compared to unsteady simulations in the time-domain and to state-of-the-art frequency-domain methods based on one-dimensional discrete Fourier transforms.
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Frey, Christian, Graham Ashcroft, Hans-Peter Kersken, and Christian Voigt. "A Harmonic Balance Technique for Multistage Turbomachinery Applications." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-25230.

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This article describes a nonlinear frequency domain method for the simulation of unsteady blade row interaction problems across several blade rows in turbomachinery. The capability to efficiently simulate such interactions is crucial for the improvement of the prediction of blade vibrations, tonal noise, and the impact of unsteadiness on aerodynamic performance. The simulation technique presented here is based on the harmonic balance approach and has been integrated into an existing flow solver. A nontrivial issue in the application of harmonic balance methods to turbomachinery flows is the fact that various fundamental frequencies may occur simultaneously in one relative system, each one being due to the interaction of two blade rows. It is shown that, considering the disturbances corresponding to different fundamental frequencies as mutually uncoupled, one can develop an unsteady simulation method which from a practial view point turns out to be highly attractive. On the one hand, it is possible to take into account arbitrarily many nonlinear interaction terms. On the other, the computational efficiency can be increased considerably once it is known that the nonlinear coupling between certain subsets of the harmonics plays only a minor role. To validate the method and demonstrate its accuracy and efficiency a multistage compressor configuration is simulated using both the method described in this article and a conventional time-domain solver.
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Zghoul, Fadi Nessir, and David Egolf. "Analyzing nonlinear circuits using a modified harmonic balance method." In 2012 International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design (SMACD). IEEE, 2012. http://dx.doi.org/10.1109/smacd.2012.6339455.

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Guillot, Louis, Pierre Vigué, Christophe Vergez, and Bruno Cochelin. "CONTINUATION OF QUASI-PERIODIC SOLUTIONS WITH TWO-FREQUENCY HARMONIC BALANCE METHOD." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2192.10775.

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Kersken, Hans-Peter, Graham Ashcroft, and Christian Frey. "A HYBRID MESH HARMONIC BALANCE SOLVER FOR THE AEROELASTIC ANALYSIS OF TURBOMACHINERY." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2346.7406.

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8

Ko, Sangho, and Robert R. Bitmead. "Identification for Nonlinear Feedback Limit-Cycle Systems Using Harmonic Balance Methods." In Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.377326.

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Lu, Junwei. "Harmonic Balance Methods used in Power Electronics and Distributed Energy System." In 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC). IEEE, 2018. http://dx.doi.org/10.1109/peac.2018.8590473.

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Chenaux, Virginie Anne, Matthias Schuff, and David Quero. "Applicability of Harmonic Balance for the Determination of Blade Stability Within the Prescribed Motion Approach." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14132.

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Abstract To predict blade aerodynamic damping during the design phase, unsteady linearized CFD methods are commonly used as they offer a reasonable accuracy at acceptable computational costs. However, for moderate blade oscillation amplitudes, nonlinear aerodynamic effects may appear, yielding eventually an evolution into a stable, limit cycle oscillation (LCO). In the perspective of raising performance and safety, identifying such scenarios might open new development possibilities. Therefore, a valuable alternative to expensive CFD time domain methods consists in applying the nonlinear frequency domain harmonic balance (HB) approach to determine the aerodynamic response. An appropriate number of higher harmonics have to be retained depending on the severity of the aerodynamic nonlinearity under consideration. This number can be identified using either a convergence study with an increasing number of harmonics, or a direct comparison with time-domain simulations. For weak to moderate aerodynamic nonlinearities, this work proposes a guideline to determine the number of harmonics without additional, comparative simulations. First, the HB convergence properties are derived using the well-known Duffing oscillator. Next, the method is applied to a compressor rotor blade subjected to a prescribed harmonic motion for conditions with and without aerodynamic nonlinearities.
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Reports on the topic "Harmonic balance methods"

1

Huang, Andy C. A harmonic balance method for PDEs. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1505342.

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