The following terms are used to describe concepts relevant to HBM analyses.
- Harmonic Balance Method (HBM)
HBM is a computational method used to solve the equations of motion of a nonlinear dynamical system in the frequency domain, which may be solved to obtain the steady-state periodic response.
- Time harmonic
Given a fundamental excitation frequency, ω, the time harmonics are the multiples: 2ω, 3ω, and so on.
- Spatial harmonic
If the model is cyclically symmetric, its response is the combination of the responses of the spatial harmonics (also called cyclic harmonic indices) that are excited by the loads. In an HBM cyclic analysis, there is a relationship between time and spatial harmonics. See Harmonic Balance Method Cyclic Equations.
- Multiharmonic solution
The multiharmonic solution of HBM equations is comprised of the system responses (amplitude and phase) at a given fundamental frequency,
(usually the frequency of applied excitation forces), as
well as time harmonics, which together represent the periodic steady-state
response.- Fundamental engine order
The engine order of the traveling wave excitation applied to the first time harmonic for an HBM cyclic analysis. The fundamental frequency of an HBM solution is the product of the fundamental engine order and the rotational speed of the excitation.
- Single stage superelement
A single stage superelement is a cyclic symmetry superelement generated for a given spatial harmonic using the multistage cyclic procedure. See also Single Stage Cyclic Symmetry Superelement CMS Example in the Substructuring Analysis Guide.
- Primary stage
If the model is cyclically symmetric with relevant cyclic harmonic greater than 0, the procedure involves using single stage superelements for the necessary harmonics. The stage superelement corresponding to the 0th harmonic is called the primary stage. All the primary loads, boundary conditions, and nonlinear elements are defined on this stage superelement.
- Alternating frequency-time (AFT)
The alternating frequency time (AFT) method, a procedure that is commonly used during HBM equation solution, enables accurate calculation of nonlinear force estimates in the time domain. During this procedure, solution estimates are converted from the frequency domain to the time domain, and the transient nonlinear forces computed in the time domain are then converted back into the frequency domain.
- Fast Fourier transform (FFT)
A fast Fourier transform (FFT) is a commonly used computational algorithm to efficiently convert a signal from the time domain to a representation in the frequency domain (forward FFT) and vice versa (backward FFT).