Matches in SemOpenAlex for { <https://semopenalex.org/work/W4324132553> ?p ?o ?g. }
Showing items 1 to 94 of
94
with 100 items per page.
- W4324132553 endingPage "110265" @default.
- W4324132553 startingPage "110265" @default.
- W4324132553 abstract "Harmonic Balance is one of the most popular methods for computing periodic solutions of nonlinear dynamical systems. In this work, we address two of its major shortcomings: First, we investigate to what extent the computational burden of stability analysis can be reduced by consistent use of Chebyshev polynomials. Second, we address the problem of a rigorous error bound, which, to the authors' knowledge, has been ignored in all engineering applications so far. Here, we rely on Urabe's error bound and, again, use Chebyshev polynomials for the computationally involved operations. We use the error estimate to automatically adjust the harmonic truncation order during numerical continuation, and confront the algorithm with a state-of-the-art adaptive Harmonic Balance implementation. Further, we rigorously prove, for the first time, the existence of some isolated periodic solutions of the forced-damped Duffing oscillator with softening characteristic. We find that the effort for obtaining a rigorous error bound, in its present form, may be too high to be useful for many engineering problems. Based on the results obtained for a sequence of numerical examples, we conclude that Chebyshev-based stability analysis indeed permits a substantial speedup. Like Harmonic Balance itself, however, this method becomes inefficient when an extremely high truncation order is needed as, e.g., in the presence of (sharply regularized) discontinuities." @default.
- W4324132553 created "2023-03-15" @default.
- W4324132553 creator A5035003811 @default.
- W4324132553 creator A5076773534 @default.
- W4324132553 date "2023-07-01" @default.
- W4324132553 modified "2023-10-14" @default.
- W4324132553 title "Are Chebyshev-based stability analysis and Urabe’s error bound useful features for Harmonic Balance?" @default.
- W4324132553 cites W1970608193 @default.
- W4324132553 cites W1980068901 @default.
- W4324132553 cites W1999969154 @default.
- W4324132553 cites W2006761896 @default.
- W4324132553 cites W2014062480 @default.
- W4324132553 cites W2018999187 @default.
- W4324132553 cites W2028566934 @default.
- W4324132553 cites W2028695297 @default.
- W4324132553 cites W2042314550 @default.
- W4324132553 cites W2050872548 @default.
- W4324132553 cites W2052771834 @default.
- W4324132553 cites W2074139192 @default.
- W4324132553 cites W2081816570 @default.
- W4324132553 cites W2090333447 @default.
- W4324132553 cites W2091468007 @default.
- W4324132553 cites W2123580041 @default.
- W4324132553 cites W2159750040 @default.
- W4324132553 cites W2161235036 @default.
- W4324132553 cites W2162408501 @default.
- W4324132553 cites W2167601371 @default.
- W4324132553 cites W2485126362 @default.
- W4324132553 cites W253052766 @default.
- W4324132553 cites W2806074878 @default.
- W4324132553 cites W2890237121 @default.
- W4324132553 cites W2990918729 @default.
- W4324132553 doi "https://doi.org/10.1016/j.ymssp.2023.110265" @default.
- W4324132553 hasPublicationYear "2023" @default.
- W4324132553 type Work @default.
- W4324132553 citedByCount "0" @default.
- W4324132553 crossrefType "journal-article" @default.
- W4324132553 hasAuthorship W4324132553A5035003811 @default.
- W4324132553 hasAuthorship W4324132553A5076773534 @default.
- W4324132553 hasBestOaLocation W43241325532 @default.
- W4324132553 hasConcept C104942944 @default.
- W4324132553 hasConcept C112972136 @default.
- W4324132553 hasConcept C11413529 @default.
- W4324132553 hasConcept C119857082 @default.
- W4324132553 hasConcept C121332964 @default.
- W4324132553 hasConcept C121758426 @default.
- W4324132553 hasConcept C127934551 @default.
- W4324132553 hasConcept C129785596 @default.
- W4324132553 hasConcept C134306372 @default.
- W4324132553 hasConcept C158622935 @default.
- W4324132553 hasConcept C21424316 @default.
- W4324132553 hasConcept C28826006 @default.
- W4324132553 hasConcept C33923547 @default.
- W4324132553 hasConcept C41008148 @default.
- W4324132553 hasConcept C62520636 @default.
- W4324132553 hasConcept C77553402 @default.
- W4324132553 hasConceptScore W4324132553C104942944 @default.
- W4324132553 hasConceptScore W4324132553C112972136 @default.
- W4324132553 hasConceptScore W4324132553C11413529 @default.
- W4324132553 hasConceptScore W4324132553C119857082 @default.
- W4324132553 hasConceptScore W4324132553C121332964 @default.
- W4324132553 hasConceptScore W4324132553C121758426 @default.
- W4324132553 hasConceptScore W4324132553C127934551 @default.
- W4324132553 hasConceptScore W4324132553C129785596 @default.
- W4324132553 hasConceptScore W4324132553C134306372 @default.
- W4324132553 hasConceptScore W4324132553C158622935 @default.
- W4324132553 hasConceptScore W4324132553C21424316 @default.
- W4324132553 hasConceptScore W4324132553C28826006 @default.
- W4324132553 hasConceptScore W4324132553C33923547 @default.
- W4324132553 hasConceptScore W4324132553C41008148 @default.
- W4324132553 hasConceptScore W4324132553C62520636 @default.
- W4324132553 hasConceptScore W4324132553C77553402 @default.
- W4324132553 hasFunder F4320320879 @default.
- W4324132553 hasLocation W43241325531 @default.
- W4324132553 hasLocation W43241325532 @default.
- W4324132553 hasLocation W43241325533 @default.
- W4324132553 hasOpenAccess W4324132553 @default.
- W4324132553 hasPrimaryLocation W43241325531 @default.
- W4324132553 hasRelatedWork W1971295149 @default.
- W4324132553 hasRelatedWork W1980926910 @default.
- W4324132553 hasRelatedWork W1993246898 @default.
- W4324132553 hasRelatedWork W2041163946 @default.
- W4324132553 hasRelatedWork W2054912819 @default.
- W4324132553 hasRelatedWork W2066466402 @default.
- W4324132553 hasRelatedWork W2094482546 @default.
- W4324132553 hasRelatedWork W2626380860 @default.
- W4324132553 hasRelatedWork W4247722846 @default.
- W4324132553 hasRelatedWork W4324132553 @default.
- W4324132553 hasVolume "194" @default.
- W4324132553 isParatext "false" @default.
- W4324132553 isRetracted "false" @default.
- W4324132553 workType "article" @default.