Harmonic field calculation by the combination of finite element analysis and harmonic balance method

Yamada, S.; Bessho, K.

doi:10.1109/20.92182

Cited by 63 publications

(35 citation statements)

References 2 publications

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“…by means of a harmonic or multiharmonic ansatz, has been pursued e.g. by Yamada and Bessho in [25] or Gyselinck et al in [14]. Other works on this topic include for example [4,11,13,18,24].…”

Section: Introductionmentioning

confidence: 99%

“…Although in some publications (e.g. [4,13,25]) this fact is exploited for rewriting the problem as a system of complex equations, we prefer to stay with the formulation over R, because the complex operator does not satisfy the Cauchy-Riemann equations and thus is not differentiable (e.g. [13,16]), what eliminates the possibility of linearization by the Newton method (cf.…”

Section: Truncated Fourier Series Expansionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical analysis of nonlinear multiharmonic eddy current problems

2005

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This work provides a complete analysis of eddy current problems, ranging from a proof of unique solvability to the analysis of a multiharmonic discretization technique.For proving existence and uniqueness, we use a Schur complement approach in order to combine the structurally different results for conducting and non-conducting regions.For solving the time-dependent problem, we take advantage of the periodicity of the solution. Since the sources usually are alternating current, we propose a truncated Fourier series expansion, i.e. a so-called multiharmonic ansatz, instead of a costly time-stepping scheme. Moreover, we suggest to introduce a regularization parameter for the numerical solution, what ensures unique solvability not only in the factor space of divergence-free functions, but in the whole space H(curl). Finally, we provide estimates for the errors that are due to the truncated Fourier series, the spatial discretization and the regularization parameter.

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Section: Introductionmentioning

confidence: 99%

Section: Truncated Fourier Series Expansionmentioning

confidence: 99%

Numerical analysis of nonlinear multiharmonic eddy current problems

2005

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“…This method is called the multiharmonic or harmonic balance finite element method [13,14,15]. This multiharmonic strategy has already been investigated to study the nonlinear vibration of electrically actuated micromembranes in vacuum [16,8,9], as well as in several other research fields [17,18,19,13,20,21]. Its effective use on large scale applications is however impeded by two main factors.…”

Section: Multiharmonic Finite Element Formulationmentioning

confidence: 99%

Steady-state, nonlinear analysis of large arrays of electrically actuated micromembranes vibrating in a fluid

Halbach

Geuzaine

2017

Engineering with Computers

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This paper describes a robust and efficient method to obtain the steady-state, nonlinear behaviour of large arrays of electrically actuated micromembranes vibrating in a fluid. The nonlinear electromechanical behavior and the multiple vibration harmonics it creates are fully taken into account thanks to a multiharmonic finite element formulation, generated automatically using symbolic calculation. A domain decomposition method allows to consider large arrays of micromembranes by efficiently distributing the computational cost on parallel computers. Two-and three-dimensional examples highlight the main properties of the proposed method.

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“…The frequency domain approach, using the harmonic balance finite-element method (HBFEM) [1], is not widely adopted as it requires the cumbersome assembly and resolution of a single but very large system of nonlinear algebraic equations. Furthermore, periodic movement cannot be easily accounted for.…”

Section: Introductionmentioning

confidence: 99%

A general method for the frequency domain FE modeling of rotating electromagnetic devices

et al. 2003

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In this paper, we present a general method to include time periodic movement in the frequency domain finite-element simulation of rotating electromagnetic (EM) devices. For the particular case of a two-dimensional (2-D) finite-element (FE) model of a rotating machine, it only requires elementary manipulations of the static moving band stiffness matrix, calculated for a number of discrete rotor positions in a fundamental period. As an application example, the no-load operation of an induction motor has been simulated. The harmonic balance results agree well with those obtained with time stepping.

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Harmonic field calculation by the combination of finite element analysis and harmonic balance method

Cited by 63 publications

References 2 publications

Numerical analysis of nonlinear multiharmonic eddy current problems

Numerical analysis of nonlinear multiharmonic eddy current problems

Steady-state, nonlinear analysis of large arrays of electrically actuated micromembranes vibrating in a fluid

A general method for the frequency domain FE modeling of rotating electromagnetic devices

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