A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions
A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I invol...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Guoqiang [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
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| Umfang: |
16 |
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| Übergeordnetes Werk: |
Enthalten in: Cancer of the uterus and treatment of incontinence (CUTI) - Robison, K.M. ELSEVIER, 2015, London |
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| Übergeordnetes Werk: |
volume:385 ; year:2016 ; day:22 ; month:12 ; pages:284-299 ; extent:16 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.jsv.2016.08.033 |
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| 520 | |a A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. | ||
| 520 | |a A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. | ||
| 700 | 1 | |a Dunne, J.F. |4 oth | |
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10.1016/j.jsv.2016.08.033 doi GBV00000000000003.pica (DE-627)ELV030090288 (ELSEVIER)S0022-460X(16)30442-4 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Chen, Guoqiang verfasserin aut A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions 2016transfer abstract 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. Dunne, J.F. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:385 year:2016 day:22 month:12 pages:284-299 extent:16 https://doi.org/10.1016/j.jsv.2016.08.033 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 385 2016 22 1222 284-299 16 045F 530 |
| spelling |
10.1016/j.jsv.2016.08.033 doi GBV00000000000003.pica (DE-627)ELV030090288 (ELSEVIER)S0022-460X(16)30442-4 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Chen, Guoqiang verfasserin aut A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions 2016transfer abstract 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. Dunne, J.F. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:385 year:2016 day:22 month:12 pages:284-299 extent:16 https://doi.org/10.1016/j.jsv.2016.08.033 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 385 2016 22 1222 284-299 16 045F 530 |
| allfields_unstemmed |
10.1016/j.jsv.2016.08.033 doi GBV00000000000003.pica (DE-627)ELV030090288 (ELSEVIER)S0022-460X(16)30442-4 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Chen, Guoqiang verfasserin aut A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions 2016transfer abstract 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. Dunne, J.F. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:385 year:2016 day:22 month:12 pages:284-299 extent:16 https://doi.org/10.1016/j.jsv.2016.08.033 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 385 2016 22 1222 284-299 16 045F 530 |
| allfieldsGer |
10.1016/j.jsv.2016.08.033 doi GBV00000000000003.pica (DE-627)ELV030090288 (ELSEVIER)S0022-460X(16)30442-4 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Chen, Guoqiang verfasserin aut A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions 2016transfer abstract 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. Dunne, J.F. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:385 year:2016 day:22 month:12 pages:284-299 extent:16 https://doi.org/10.1016/j.jsv.2016.08.033 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 385 2016 22 1222 284-299 16 045F 530 |
| allfieldsSound |
10.1016/j.jsv.2016.08.033 doi GBV00000000000003.pica (DE-627)ELV030090288 (ELSEVIER)S0022-460X(16)30442-4 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Chen, Guoqiang verfasserin aut A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions 2016transfer abstract 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. Dunne, J.F. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:385 year:2016 day:22 month:12 pages:284-299 extent:16 https://doi.org/10.1016/j.jsv.2016.08.033 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 385 2016 22 1222 284-299 16 045F 530 |
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a fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions |
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A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions |
| abstract |
A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. |
| abstractGer |
A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. |
| abstract_unstemmed |
A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency. |
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A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions |
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