Matches in SemOpenAlex for { <https://semopenalex.org/work/W2067993030> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W2067993030 endingPage "1051" @default.
- W2067993030 startingPage "1045" @default.
- W2067993030 abstract "The Duffing equation ẍ+αx+βx3 = F cosωt (α>0) is known to possess periodic solutions with frequency ω/n for all integral n, provided that β is sufficiently small. For n=1 and n≠1, these solutions are designated in the literature as harmonic and subharmonic solutions respectively. In this paper, a classification of the various types of periodic solutions is given, in which it is shown that there are two types of harmonic solutions and two types of subharmonic solutions for sufficiently small β. The perturbation method is employed to find the approximate response curves for each of the four types of periodic solutions. A comparison is made between the response curves obtained in the non-linear case (β≠0) and linear case (β=0) and some properties of the solutions in the non-linear case are discussed. A comparison is then made between the perturbation method and the Rauscher method, which is an iteration method that assumes F small instead of β. This comparison is not made in all generality, but only for one particular type of subharmonic solution. The main result obtained is that for F small, the two methods yield similar results for larger values of β than might have been anticipated." @default.
- W2067993030 created "2016-06-24" @default.
- W2067993030 creator A5012269140 @default.
- W2067993030 date "1949-11-01" @default.
- W2067993030 modified "2023-09-27" @default.
- W2067993030 title "Harmonic and Subharmonic Response for the Duffing Equation <i>ẍ</i>+α<i>x</i>+β<i>x</i><sup>3</sup> = <i>F</i> cosω<i>t</i> (α>0)" @default.
- W2067993030 cites W1521327797 @default.
- W2067993030 cites W1530136772 @default.
- W2067993030 cites W1991944832 @default.
- W2067993030 cites W2050705093 @default.
- W2067993030 cites W2094312257 @default.
- W2067993030 cites W2591453328 @default.
- W2067993030 cites W1524455105 @default.
- W2067993030 doi "https://doi.org/10.1063/1.1698272" @default.
- W2067993030 hasPublicationYear "1949" @default.
- W2067993030 type Work @default.
- W2067993030 sameAs 2067993030 @default.
- W2067993030 citedByCount "13" @default.
- W2067993030 countsByYear W20679930302012 @default.
- W2067993030 countsByYear W20679930302014 @default.
- W2067993030 countsByYear W20679930302016 @default.
- W2067993030 countsByYear W20679930302018 @default.
- W2067993030 countsByYear W20679930302020 @default.
- W2067993030 countsByYear W20679930302022 @default.
- W2067993030 countsByYear W20679930302023 @default.
- W2067993030 crossrefType "journal-article" @default.
- W2067993030 hasAuthorship W2067993030A5012269140 @default.
- W2067993030 hasBestOaLocation W20679930301 @default.
- W2067993030 hasConcept C121332964 @default.
- W2067993030 hasConcept C127934551 @default.
- W2067993030 hasConcept C134306372 @default.
- W2067993030 hasConcept C158622935 @default.
- W2067993030 hasConcept C177918212 @default.
- W2067993030 hasConcept C193687819 @default.
- W2067993030 hasConcept C33923547 @default.
- W2067993030 hasConcept C5555538 @default.
- W2067993030 hasConcept C62520636 @default.
- W2067993030 hasConceptScore W2067993030C121332964 @default.
- W2067993030 hasConceptScore W2067993030C127934551 @default.
- W2067993030 hasConceptScore W2067993030C134306372 @default.
- W2067993030 hasConceptScore W2067993030C158622935 @default.
- W2067993030 hasConceptScore W2067993030C177918212 @default.
- W2067993030 hasConceptScore W2067993030C193687819 @default.
- W2067993030 hasConceptScore W2067993030C33923547 @default.
- W2067993030 hasConceptScore W2067993030C5555538 @default.
- W2067993030 hasConceptScore W2067993030C62520636 @default.
- W2067993030 hasIssue "11" @default.
- W2067993030 hasLocation W20679930301 @default.
- W2067993030 hasOpenAccess W2067993030 @default.
- W2067993030 hasPrimaryLocation W20679930301 @default.
- W2067993030 hasRelatedWork W1987239085 @default.
- W2067993030 hasRelatedWork W1996704977 @default.
- W2067993030 hasRelatedWork W2015847813 @default.
- W2067993030 hasRelatedWork W2040052123 @default.
- W2067993030 hasRelatedWork W2137425985 @default.
- W2067993030 hasRelatedWork W2358205793 @default.
- W2067993030 hasRelatedWork W2895593156 @default.
- W2067993030 hasRelatedWork W3141539650 @default.
- W2067993030 hasRelatedWork W3145537319 @default.
- W2067993030 hasRelatedWork W4236677659 @default.
- W2067993030 hasVolume "20" @default.
- W2067993030 isParatext "false" @default.
- W2067993030 isRetracted "false" @default.
- W2067993030 magId "2067993030" @default.
- W2067993030 workType "article" @default.