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001 978-3-030-23803-2
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005 20220801213906.0
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008 190905s2020 sz | s |||| 0|eng d
020 _a9783030238032
_9978-3-030-23803-2
024 7 _a10.1007/978-3-030-23803-2
_2doi
050 4 _aTA349-359
072 7 _aTGB
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aTGB
_2thema
082 0 4 _a620.1
_223
100 1 _aBanichuk, Nikolay.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_935026
245 1 0 _aStability of Axially Moving Materials
_h[electronic resource] /
_cby Nikolay Banichuk, Alexander Barsuk, Juha Jeronen, Tero Tuovinen, Pekka Neittaanmäki.
250 _a1st ed. 2020.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2020.
300 _aXI, 642 p. 175 illus., 40 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSolid Mechanics and Its Applications,
_x2214-7764 ;
_v259
505 0 _aPreface -- 1. Prototype Problems: Bifurcations of Different Kinds -- 1.1 Rigid column with elastic clamping -- 1.2 Elastic column and its optimization -- 1.3 Elastic rod under torsion -- 1.4 Divergence and optimization of wings -- 1.5 Stability of tensioned cantilever beam -- 1.6 Accelerating motion of rod (rocket, missile) under follower force -- 2 Bifurcation Analysis for Polynomial Equations -- 2.1 Bifurcation and parametric representations -- 2.2 Analysis of a cubic equation -- 2.3 Analysis of a quartic (fourth-order) polynomial equation -- 3 Nonconservative Systems with a Finite Number of Degrees of Freedom -- 3.1 Critical parameters and destabilizing perturbations -- 3.2 Characteristic polynomial and series expansions -- 3.3 Ideal perturbations and sufficient conditions for stability (n = 2) -- 3.4 Matrices and examples of ideal perturbations -- 3.5 Stability of systems subjected to deficient perturbations and determination of the deficiency index -- 3.6 On the stability and trajectories of the double pendulum with linear springs and dampers -- 4 Some General Methods -- 4.1 Criteria of elastic stability -- 4.2 Bifurcations and multiplicity of critical loads -- 4.3 Decomposition method for bimodal solutions -- 4.4 Bifurcation and analysis of implicitly given functionals -- 4.5 Variational principle and bifurcation analysis -- 5 Modeling and Stability Analysis of Axially Moving Materials -- 5.1 General dynamics and geometric considerations -- 5.2 Kinematic relations of small deformations -- 5.3 Constitutive linear elastic and visco-elastic relations -- 5.4 Modeling of beams and panels -- 5.5 Modeling of axially moving materials -- 5.6 Transformation to weak form -- 5.7 Boundary conditions -- 5.8 Numerical examples in stability of axially moving elastic and viscoelastic panels -- 6 Stability of Axially Moving Plates -- 6.1 Isotropic plates -- 6.2 Orthotropic plates -- 6.3 Plates with a nonuniform axial tension distribution -- 7 Stability of Axially Moving Strings, Beams and Panels -- 7.1 Unified model and exact eigensolutions for torsional, longitudinal and transverse vibration types -- 7.2 Exact eigensolutions of the traveling string with damping -- 7.3 Exact eigensolutions of axially moving beams and panels -- 7.4 Long axially moving beam with periodic elastic supports -- 7.5 Stability of a traveling beam in a gravitational field -- 8 Stability in Fluid–Structure Interaction of Axially Moving Materials -- 8.1 Basic concepts -- 8.2 Analytical solution of two-dimensional potential flow -- 8.3 Added-mass approximation -- 8.4 Numerical examples -- 8.5 Recommendations for further reading -- 9 Optimization of Elastic Bodies Subjected to Thermal Loads -- 9.1 Optimal distribution of thickness in a thermoelastic beam -- 9.2 Optimal distribution of materials in a thermoelastic beam -- 9.3 A guaranteed double-sided estimate for energy dissipation in heat conduction of locally orthotropic solid bodies -- 9.4 Conclusion -- Appendix A Cartesian tensors -- A.1 Tensor algebra -- A.2 Tensor calculus -- A.3 Integration by parts in multiple dimensions -- Appendix B Numerical integration of ODEs and semidiscrete PDEs -- B.1 Explicit Runge–Kutta methods -- B.2 Classical implicit methods -- B.3 The theoretical basis of iterative implicit methods -- B.4 Time-discontinuous Galerkin (dG) -- C Finite elements of the Hermite type -- Appendix C: Finite elements of the Hermite type -- C.1 Coordinate mapping and the derivative degrees of freedom.
520 _aThis book discusses the stability of axially moving materials, which are encountered in process industry applications such as papermaking. A special emphasis is given to analytical and semianalytical approaches. As preliminaries, we consider a variety of problems across mechanics involving bifurcations, allowing to introduce the techniques in a simplified setting. In the main part of the book, the fundamentals of the theory of axially moving materials are presented in a systematic manner, including both elastic and viscoelastic material models, and the connection between the beam and panel models. The issues that arise in formulating boundary conditions specifically for axially moving materials are discussed. Some problems involving axially moving isotropic and orthotropic elastic plates are analyzed. Analytical free-vibration solutions for axially moving strings with and without damping are derived. A simple model for fluid--structure interaction of an axially moving panel is presented in detail. This book is addressed to researchers, industrial specialists and students in the fields of theoretical and applied mechanics, and of applied and computational mathematics.
650 0 _aMechanics, Applied.
_93253
650 0 _aMathematical optimization.
_94112
650 0 _aMathematics—Data processing.
_931594
650 0 _aManufactures.
_931642
650 1 4 _aEngineering Mechanics.
_931830
650 2 4 _aOptimization.
_935027
650 2 4 _aComputational Mathematics and Numerical Analysis.
_931598
650 2 4 _aMachines, Tools, Processes.
_931645
700 1 _aBarsuk, Alexander.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_935028
700 1 _aJeronen, Juha.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_935029
700 1 _aTuovinen, Tero.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_935030
700 1 _aNeittaanmäki, Pekka.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_935031
710 2 _aSpringerLink (Online service)
_935032
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030238025
776 0 8 _iPrinted edition:
_z9783030238049
776 0 8 _iPrinted edition:
_z9783030238056
830 0 _aSolid Mechanics and Its Applications,
_x2214-7764 ;
_v259
_935033
856 4 0 _uhttps://doi.org/10.1007/978-3-030-23803-2
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c75720
_d75720