The effects of nonlinear damping on degenerate parametric amplification
This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase between the two. This generalizes and expands on previous studie...
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| Veröffentlicht in: | Nonlinear dynamics 2020-12, Vol.102 (4), p.2433-2452 |
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| creator | Li, Donghao Shaw, Steven W. |
| description | This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase between the two. This generalizes and expands on previous studies of nonlinear effects on parametric amplification, notably by including the effects of nonlinear damping, which is commonly observed in a large variety of systems, including micro- and nano-scale resonators. Using the method of averaging, a thorough parameter study is carried out that describes the effects of the amplitudes and relative phase of the two forms of excitation. The effects of nonlinear damping on the parametric gain are first derived. The transitions among various topological forms of the frequency response curves, which can include isolae, dual peaks, and loops, are determined, and bifurcation analyses in parameter spaces of interest are carried out. In general, these results provide a complete picture of the system response and allow one to select drive conditions of interest that avoid bistability while providing maximum amplitude gain, maximum phase sensitivity, or a flat resonant peak, in systems with nonlinear damping. |
| doi_str_mv | 10.1007/s11071-020-06090-8 |
| format | Article |
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This generalizes and expands on previous studies of nonlinear effects on parametric amplification, notably by including the effects of nonlinear damping, which is commonly observed in a large variety of systems, including micro- and nano-scale resonators. Using the method of averaging, a thorough parameter study is carried out that describes the effects of the amplitudes and relative phase of the two forms of excitation. The effects of nonlinear damping on the parametric gain are first derived. The transitions among various topological forms of the frequency response curves, which can include isolae, dual peaks, and loops, are determined, and bifurcation analyses in parameter spaces of interest are carried out. In general, these results provide a complete picture of the system response and allow one to select drive conditions of interest that avoid bistability while providing maximum amplitude gain, maximum phase sensitivity, or a flat resonant peak, in systems with nonlinear damping.</description><identifier>ISSN: 0924-090X</identifier><identifier>EISSN: 1573-269X</identifier><identifier>DOI: 10.1007/s11071-020-06090-8</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Amplification ; Amplitudes ; Automotive Engineering ; Bistability ; Classical Mechanics ; Control ; Damping ; Dynamic response ; Dynamical Systems ; Engineering ; Engineering, Mechanical ; Excitation ; Frequency response ; Mechanical Engineering ; Mechanics ; Nonlinear systems ; Original Paper ; Parameters ; Science & Technology ; Stiffness ; Technology ; Vibration</subject><ispartof>Nonlinear dynamics, 2020-12, Vol.102 (4), p.2433-2452</ispartof><rights>The Author(s) 2020</rights><rights>The Author(s) 2020. 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This generalizes and expands on previous studies of nonlinear effects on parametric amplification, notably by including the effects of nonlinear damping, which is commonly observed in a large variety of systems, including micro- and nano-scale resonators. Using the method of averaging, a thorough parameter study is carried out that describes the effects of the amplitudes and relative phase of the two forms of excitation. The effects of nonlinear damping on the parametric gain are first derived. The transitions among various topological forms of the frequency response curves, which can include isolae, dual peaks, and loops, are determined, and bifurcation analyses in parameter spaces of interest are carried out. In general, these results provide a complete picture of the system response and allow one to select drive conditions of interest that avoid bistability while providing maximum amplitude gain, maximum phase sensitivity, or a flat resonant peak, in systems with nonlinear damping.</description><subject>Amplification</subject><subject>Amplitudes</subject><subject>Automotive Engineering</subject><subject>Bistability</subject><subject>Classical Mechanics</subject><subject>Control</subject><subject>Damping</subject><subject>Dynamic response</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Engineering, Mechanical</subject><subject>Excitation</subject><subject>Frequency response</subject><subject>Mechanical Engineering</subject><subject>Mechanics</subject><subject>Nonlinear systems</subject><subject>Original Paper</subject><subject>Parameters</subject><subject>Science & Technology</subject><subject>Stiffness</subject><subject>Technology</subject><subject>Vibration</subject><issn>0924-090X</issn><issn>1573-269X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>AOWDO</sourceid><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNkMFOAyEURYnRxFr9AVeTuDSjD5gOsDSNVpMmbmrSHWGYN5WmhQrTGP9e6hjdGVdA3j3APYRcUrihAOI2UQqClsCghBoUlPKIjOhE8JLVanlMRqBYVebB8pScpbQGAM5Ajshs8YoFdh3aPhWhK3zwG-fRxKI1253zqyL4osUVeoymx2JnotliH50t8nzjOmdN74I_Jyed2SS8-F7H5OXhfjF9LOfPs6fp3by0vOZ9KaltkDYCkUneCi4pb9FIISh0ILGijaqF4IzlVi1UDTucBHCF3FS0snxMroZ7dzG87TH1eh320ecnNasE51xxxXKKDSkbQ0oRO72Lbmvih6agD8L0IExnYfpLmJYZkgP0jk3oknXoLf6A2dhEKWCszjugU9d_9Z6Gve8zev1_NKf5kE454VcYfzv88b1PETKNag</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Li, Donghao</creator><creator>Shaw, Steven W.</creator><general>Springer Netherlands</general><general>Springer Nature</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AOWDO</scope><scope>BLEPL</scope><scope>DTL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0002-3874-4828</orcidid><orcidid>https://orcid.org/0000-0002-4853-9027</orcidid></search><sort><creationdate>20201201</creationdate><title>The effects of nonlinear damping on degenerate parametric amplification</title><author>Li, Donghao ; Shaw, Steven W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-81cbe1b7ee283d73813dea87710f08e41b9677322100d04b267737039e3a414c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Amplification</topic><topic>Amplitudes</topic><topic>Automotive Engineering</topic><topic>Bistability</topic><topic>Classical Mechanics</topic><topic>Control</topic><topic>Damping</topic><topic>Dynamic response</topic><topic>Dynamical Systems</topic><topic>Engineering</topic><topic>Engineering, Mechanical</topic><topic>Excitation</topic><topic>Frequency response</topic><topic>Mechanical Engineering</topic><topic>Mechanics</topic><topic>Nonlinear systems</topic><topic>Original Paper</topic><topic>Parameters</topic><topic>Science & Technology</topic><topic>Stiffness</topic><topic>Technology</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Donghao</creatorcontrib><creatorcontrib>Shaw, Steven W.</creatorcontrib><collection>Springer Nature OA/Free Journals</collection><collection>Web of Science - Science Citation Index Expanded - 2020</collection><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Proquest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Nonlinear dynamics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Donghao</au><au>Shaw, Steven W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The effects of nonlinear damping on degenerate parametric amplification</atitle><jtitle>Nonlinear dynamics</jtitle><stitle>Nonlinear Dyn</stitle><stitle>NONLINEAR DYNAM</stitle><date>2020-12-01</date><risdate>2020</risdate><volume>102</volume><issue>4</issue><spage>2433</spage><epage>2452</epage><pages>2433-2452</pages><issn>0924-090X</issn><eissn>1573-269X</eissn><abstract>This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase between the two. 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| subjects | Amplification Amplitudes Automotive Engineering Bistability Classical Mechanics Control Damping Dynamic response Dynamical Systems Engineering Engineering, Mechanical Excitation Frequency response Mechanical Engineering Mechanics Nonlinear systems Original Paper Parameters Science & Technology Stiffness Technology Vibration |
| title | The effects of nonlinear damping on degenerate parametric amplification |
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