On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle
Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may mov...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Andrews, Kevin T. [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
1996 |
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| Anmerkung: |
© Kluwer Academic Publishers 1996 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of elasticity - Kluwer Academic Publishers, 1971, 42(1996), 1 vom: Jan., Seite 1-30 |
|---|---|
| Übergeordnetes Werk: |
volume:42 ; year:1996 ; number:1 ; month:01 ; pages:1-30 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF00041221 |
|---|
| Katalog-ID: |
OLC2113189895 |
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| 245 | 1 | 0 | |a On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle |
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| 520 | |a Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. | ||
| 700 | 1 | |a Shillor, M. |4 aut | |
| 700 | 1 | |a Wright, S. |4 aut | |
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10.1007/BF00041221 doi (DE-627)OLC2113189895 (DE-He213)BF00041221-p DE-627 ger DE-627 rakwb eng 600 VZ Andrews, Kevin T. verfasserin aut On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1996 Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. Shillor, M. aut Wright, S. aut Enthalten in Journal of elasticity Kluwer Academic Publishers, 1971 42(1996), 1 vom: Jan., Seite 1-30 (DE-627)129297275 (DE-600)121407-X (DE-576)014490439 0374-3535 nnns volume:42 year:1996 number:1 month:01 pages:1-30 https://doi.org/10.1007/BF00041221 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2409 GBV_ILN_4046 GBV_ILN_4700 AR 42 1996 1 01 1-30 |
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10.1007/BF00041221 doi (DE-627)OLC2113189895 (DE-He213)BF00041221-p DE-627 ger DE-627 rakwb eng 600 VZ Andrews, Kevin T. verfasserin aut On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1996 Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. Shillor, M. aut Wright, S. aut Enthalten in Journal of elasticity Kluwer Academic Publishers, 1971 42(1996), 1 vom: Jan., Seite 1-30 (DE-627)129297275 (DE-600)121407-X (DE-576)014490439 0374-3535 nnns volume:42 year:1996 number:1 month:01 pages:1-30 https://doi.org/10.1007/BF00041221 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2409 GBV_ILN_4046 GBV_ILN_4700 AR 42 1996 1 01 1-30 |
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10.1007/BF00041221 doi (DE-627)OLC2113189895 (DE-He213)BF00041221-p DE-627 ger DE-627 rakwb eng 600 VZ Andrews, Kevin T. verfasserin aut On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1996 Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. Shillor, M. aut Wright, S. aut Enthalten in Journal of elasticity Kluwer Academic Publishers, 1971 42(1996), 1 vom: Jan., Seite 1-30 (DE-627)129297275 (DE-600)121407-X (DE-576)014490439 0374-3535 nnns volume:42 year:1996 number:1 month:01 pages:1-30 https://doi.org/10.1007/BF00041221 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2409 GBV_ILN_4046 GBV_ILN_4700 AR 42 1996 1 01 1-30 |
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10.1007/BF00041221 doi (DE-627)OLC2113189895 (DE-He213)BF00041221-p DE-627 ger DE-627 rakwb eng 600 VZ Andrews, Kevin T. verfasserin aut On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1996 Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. Shillor, M. aut Wright, S. aut Enthalten in Journal of elasticity Kluwer Academic Publishers, 1971 42(1996), 1 vom: Jan., Seite 1-30 (DE-627)129297275 (DE-600)121407-X (DE-576)014490439 0374-3535 nnns volume:42 year:1996 number:1 month:01 pages:1-30 https://doi.org/10.1007/BF00041221 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2409 GBV_ILN_4046 GBV_ILN_4700 AR 42 1996 1 01 1-30 |
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10.1007/BF00041221 doi (DE-627)OLC2113189895 (DE-He213)BF00041221-p DE-627 ger DE-627 rakwb eng 600 VZ Andrews, Kevin T. verfasserin aut On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1996 Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. Shillor, M. aut Wright, S. aut Enthalten in Journal of elasticity Kluwer Academic Publishers, 1971 42(1996), 1 vom: Jan., Seite 1-30 (DE-627)129297275 (DE-600)121407-X (DE-576)014490439 0374-3535 nnns volume:42 year:1996 number:1 month:01 pages:1-30 https://doi.org/10.1007/BF00041221 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2409 GBV_ILN_4046 GBV_ILN_4700 AR 42 1996 1 01 1-30 |
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Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. © Kluwer Academic Publishers 1996 |
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Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. © Kluwer Academic Publishers 1996 |
| abstract_unstemmed |
Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized. © Kluwer Academic Publishers 1996 |
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10.1007/BF00041221 |
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2024-07-03T17:58:29.080Z |
| _version_ |
1803581662516215808 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2113189895</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503051350.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230503s1996 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/BF00041221</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2113189895</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)BF00041221-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">600</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Andrews, Kevin T.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1996</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">© Kluwer Academic Publishers 1996</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. 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