Talk:Harmonic balance

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Disputed

Latest comment: 3 years ago2 comments1 person in discussion

Possible misattribution

The article starts out saying, that the Harmonic Balance methods was originally introduced by Michel Nahkla. Looking at the given reference ^[1] however, in the paper's introduction one can find: "..., the harmonic balance method as originally implemented by Baily^[2] and Lindenlaub ^[3]...".

Being newly registered I want to ask for advice, if and how this should be corrected. Standing on its own, it looks like a mis-attribution of the method. It is particularly curious because the change adding this attribution was done by a user Mikey1720, who has also added some curiously flattering words to the article about Michel Nakhla, and didn't make much of other contributions to Wikipedia, making it look a lot like an edit by the author himself.

--Editeditit (talk) 10:11, 29 September 2021 (UTC)Reply

Possibly overly specific

Additionally, literature seems to use the terminology of "harmonic balance" or "balancing the harmonics" in a more general sense:

Given an equation

F(t,x(t),{\dot {x}}(t))=0

that has been rewritten in terms of coefficients $x_{k}$ as

\sum _{j}F_{j}(\{x_{k}\})e^{i\omega (j)t}=0,

where any number of terms $F_{j}$ may have the same frequency $\omega (j)$ .

Be $\{\omega _{k}\}$ the set of unique frequencies appearing above.

Then the terminology "balancing the harmonics" or "harmonic balance" is used to describe the two steps of using linear-independence of the functions $e^{i\omega _{k}t}$ to (a) group terms with equal frequencies $\omega _{k}$ together into a single expression

\sum _{j}^{\omega (j)=\omega _{k}}\left(F_{j}(\{x_{k'}\})\right)e^{i\omega _{k}t}

and (b) set the time-independent part of each expression equal to zero, thereby obtaining an equation system

\sum _{j}^{\omega (j)=\omega _{k}}F_{j}(\{x_{k'}\})=0\qquad \forall \omega _{k}.

One example of such usage of the terminology is this lecture, but also the way the terminology is used by Nakhla and Vlach ^[1]. I didn't have access to their references by Baily ^[2] and Lindenlaub ^[3], so I couldn't yet find earlier mentions of the "harmonic balance" terminology.

Additionally, the equivalent German terminology of "Harmonische Balance" seems to be used quite differently. I wasn't yet able to verify how strongly the articles are related.

--Editeditit (talk) 13:21, 1 October 2021 (UTC)Reply

References

^ ^a ^b Nakhla, Michel S.; Vlach, Jiri (February 1976). "A piecewise harmonic balance technique for determination of periodic response of nonlinear systems". IEEE Transactions on Circuits and Systems. CAS-23: 85–91. ISSN 0098-4094.
^ ^a ^b E. M. Baily, “Steady state harmonic analysis of nonlinear net- works,” Ph.D. dissertation, Stanford Univ., Stanford, CA, 1968.
^ ^a ^b J. C. Lindenlaub, “An approach for finding the sinusoidal steady state response of nonlinear systems,” in Proc. 7th Ann. Allerton Conf. Circuit and System Theory, Univ. Illinois, Chicago, 1969.

Add topic

[Nakhla1976-1] Nakhla, Michel S.; Vlach, Jiri (February 1976). "A piecewise harmonic balance technique for determination of periodic response of nonlinear systems". IEEE Transactions on Circuits and Systems. CAS-23: 85–91. ISSN 0098-4094.

[Baily1968-2] E. M. Baily, “Steady state harmonic analysis of nonlinear net- works,” Ph.D. dissertation, Stanford Univ., Stanford, CA, 1968.

[Lindenlaub1969-3] J. C. Lindenlaub, “An approach for finding the sinusoidal steady state response of nonlinear systems,” in Proc. 7th Ann. Allerton Conf. Circuit and System Theory, Univ. Illinois, Chicago, 1969.

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