Linear dynamical analysis of fractionally damped beams and rods
Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a w...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dönmez Demir, D. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of engineering mathematics - Springer Netherlands, 1967, 85(2013), 1 vom: 16. Juli, Seite 131-147 |
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| Übergeordnetes Werk: |
volume:85 ; year:2013 ; number:1 ; day:16 ; month:07 ; pages:131-147 |
| Links: |
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| DOI / URN: |
10.1007/s10665-013-9642-9 |
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OLC2074044593 |
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| 520 | |a Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. | ||
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| 650 | 4 | |a Method of multiple scales | |
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| 700 | 1 | |a Sınır, B. G. |4 aut | |
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10.1007/s10665-013-9642-9 doi (DE-627)OLC2074044593 (DE-He213)s10665-013-9642-9-p DE-627 ger DE-627 rakwb eng 510 VZ Dönmez Demir, D. verfasserin aut Linear dynamical analysis of fractionally damped beams and rods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. Fractional damping Method of multiple scales Perturbation method Viscoelastic beam Bildik, N. aut Sınır, B. G. aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 85(2013), 1 vom: 16. Juli, Seite 131-147 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:85 year:2013 number:1 day:16 month:07 pages:131-147 https://doi.org/10.1007/s10665-013-9642-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4700 AR 85 2013 1 16 07 131-147 |
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10.1007/s10665-013-9642-9 doi (DE-627)OLC2074044593 (DE-He213)s10665-013-9642-9-p DE-627 ger DE-627 rakwb eng 510 VZ Dönmez Demir, D. verfasserin aut Linear dynamical analysis of fractionally damped beams and rods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. Fractional damping Method of multiple scales Perturbation method Viscoelastic beam Bildik, N. aut Sınır, B. G. aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 85(2013), 1 vom: 16. Juli, Seite 131-147 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:85 year:2013 number:1 day:16 month:07 pages:131-147 https://doi.org/10.1007/s10665-013-9642-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4700 AR 85 2013 1 16 07 131-147 |
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10.1007/s10665-013-9642-9 doi (DE-627)OLC2074044593 (DE-He213)s10665-013-9642-9-p DE-627 ger DE-627 rakwb eng 510 VZ Dönmez Demir, D. verfasserin aut Linear dynamical analysis of fractionally damped beams and rods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. Fractional damping Method of multiple scales Perturbation method Viscoelastic beam Bildik, N. aut Sınır, B. G. aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 85(2013), 1 vom: 16. Juli, Seite 131-147 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:85 year:2013 number:1 day:16 month:07 pages:131-147 https://doi.org/10.1007/s10665-013-9642-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4700 AR 85 2013 1 16 07 131-147 |
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10.1007/s10665-013-9642-9 doi (DE-627)OLC2074044593 (DE-He213)s10665-013-9642-9-p DE-627 ger DE-627 rakwb eng 510 VZ Dönmez Demir, D. verfasserin aut Linear dynamical analysis of fractionally damped beams and rods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. Fractional damping Method of multiple scales Perturbation method Viscoelastic beam Bildik, N. aut Sınır, B. G. aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 85(2013), 1 vom: 16. Juli, Seite 131-147 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:85 year:2013 number:1 day:16 month:07 pages:131-147 https://doi.org/10.1007/s10665-013-9642-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4700 AR 85 2013 1 16 07 131-147 |
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10.1007/s10665-013-9642-9 doi (DE-627)OLC2074044593 (DE-He213)s10665-013-9642-9-p DE-627 ger DE-627 rakwb eng 510 VZ Dönmez Demir, D. verfasserin aut Linear dynamical analysis of fractionally damped beams and rods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. Fractional damping Method of multiple scales Perturbation method Viscoelastic beam Bildik, N. aut Sınır, B. G. aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 85(2013), 1 vom: 16. Juli, Seite 131-147 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:85 year:2013 number:1 day:16 month:07 pages:131-147 https://doi.org/10.1007/s10665-013-9642-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4700 AR 85 2013 1 16 07 131-147 |
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Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. © Springer Science+Business Media Dordrecht 2013 |
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Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. © Springer Science+Business Media Dordrecht 2013 |
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Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. © Springer Science+Business Media Dordrecht 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2074044593</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503052739.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10665-013-9642-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2074044593</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10665-013-9642-9-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dönmez Demir, D.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Linear dynamical analysis of fractionally damped beams and rods</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media Dordrecht 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional damping</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Method of multiple scales</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Perturbation method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Viscoelastic beam</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bildik, N.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sınır, B. G.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of engineering mathematics</subfield><subfield code="d">Springer Netherlands, 1967</subfield><subfield code="g">85(2013), 1 vom: 16. 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