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ns1:datePublished "2014-09-10" ;
ns1:datePublishedReg "2014-09-10" ;
ns1:description "This chapter is aimed on investigation of non-linear dynamics of conical and spherical shells. The variational equations are derived, and then the problem is reduced to a set of non-linear ordinary differential and algebraic equations. Since further axially symmetric deformation of closed shallow rotational shells and circled plates subjected to uniformly distributed periodic load being normal to the middle plate/shell surface are studied, the polar co-ordinates are used and four types of boundary conditions are investigated. The obtained equations are solved numerically, and the results reliability and validity are discussed in either regular, bifurcation or chaotic regimes including constant and non-constant thickness of the mentioned structural members, taking into account an initial imperfection/deflection. The classical approaches (time histories and frequency power spectra) are used to monitor different transitions from periodic to chaotic vibrations. Novel non-linear dynamical phenomena exhibited by the studied plates/shells are detected and discussed versus the chosen control parameters. In particular, the so called vibration type charts (amplitude—frequency of excitation planes) versus the different shell slopes are reported, which are of a particular importance for direct engineering applications. Finally, it is demonstrated how one may control non-linear dynamics of the studied continuous systems by using their thickness, in order to avoid buckling and stability loss phenomena." ;
ns1:editor ( [ a ns1:Person ;
ns1:familyName "Altenbach" ;
ns1:givenName "Holm" ] [ a ns1:Person ;
ns1:familyName "Mikhasev" ;
ns1:givenName "Gennadi I." ] ) ;
ns1:genre "chapter" ;
ns1:inLanguage "en" ;
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ns1:isbn "978-3-319-02534-6",
"978-3-319-02535-3" ;
ns1:name "Shell and Membrane Theories in Mechanics and Biology" ] ;
ns1:keywords "Novel non-linear dynamical phenomena",
"Polar",
"account",
"algebraic equations",
"applications",
"approach",
"bifurcation",
"boundary conditions",
"chaotic regime",
"chaotic vibrations",
"chapter",
"charts",
"classical approach",
"closed shallow rotational shells",
"conditions",
"conical",
"continuous system",
"control",
"control parameters",
"deflection",
"deformation",
"different shell slopes",
"different transitions",
"differential",
"direct engineering applications",
"dynamical phenomena",
"dynamics",
"engineering applications",
"equations",
"imperfection/deflection",
"importance",
"initial imperfection/deflection",
"investigation",
"load",
"loss phenomenon",
"members",
"middle plate/shell surface",
"non-constant thickness",
"non-linear dynamical phenomena",
"non-linear dynamics",
"non-linear ordinary differential",
"order",
"ordinary differential",
"parameters",
"particular importance",
"periodic load",
"phenomenon",
"plate",
"plate/shell surface",
"plates/shells",
"problem",
"regime",
"reliability",
"result reliability",
"rotational shells",
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"shallow rotational shells",
"shell",
"shell slopes",
"shell surface",
"slope",
"spherical shell",
"stability loss phenomena",
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ns1:name "Chaotic Vibrations of Conical and Spherical Shells and Their Control" ;
ns1:pagination "59-80" ;
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ns1:name "doi" ;
ns1:value "10.1007/978-3-319-02535-3_3" ],
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ns1:value "pub.1007477928" ] ;
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ns1:name "Springer Nature" ] ;
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ns1:sdDatePublished "2022-01-01T19:17" ;
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ns1:url "https://doi.org/10.1007/978-3-319-02535-3_3" ;
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ns1:name "Mathematical Sciences" .
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ns1:name "Pure Mathematics" .
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ns1:affiliation ;
ns1:familyName "Awrejcewicz" ;
ns1:givenName "Jan" ;
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a ns1:Person ;
ns1:affiliation ;
ns1:familyName "Krysko" ;
ns1:givenName "Vadim A." ;
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ns1:alternateName "Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski Str., 90-924, Łódź, Poland" ;
ns1:name "Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski Str., 90-924, Łódź, Poland" .
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ns1:alternateName "Department of Mathematics and Modeling, Saratov State Technical University, Politekhnicheskaya 77, 410054, Saratov, Russia" ;
ns1:name "Department of Mathematics and Modeling, Saratov State Technical University, Politekhnicheskaya 77, 410054, Saratov, Russia" .