LEADER 01830nam 2200469 450 001 000005115 005 20150219101058.0 010 $a2-251-00453-X 100 $a20150219d1997----km-y0itay0103----ba 101 2 $agrc$aarm$afre 102 $aFR 200 1 $aProgymnasmata$fAelius Théon$gtexte établi et traduit par Michel Patillon$gavec l' assistance, pour l'Arménien, de Giancarlo Bolognesi 210 $aParis$c<> belles lettres$d1997 215 $aCLVI, 234 p.$d20 cm. 225 2 $aCollection des universités de France 300 $aTraduzione francese con testo greco e armeno a fronte 410 0$12001$aCollection des universités de France 500 11$aProgymnasmata / Theon, Aelius$913504 676 $a885.01$v(22. ed.)$9Discorsi in greco classico. 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Vibrations of Continuous Elastic Solid Media; 1.1. Objective of the chapter; 1.2. Equations of motion and boundary conditions of continuous media; 1.2.1. Description of the movement of continuous media; 1.2.2. Law of conservation; 1.2.3. Conservation of mass; 1.2.4. Conservation of momentum; 1.2.5. Conservation of energy; 1.2.6. Boundary conditions; 1.3. Study of the vibrations: small movements around a position of static, stable equilibrium 327 $a1.3.1. Linearization around a configuration of reference1.3.2. Elastic solid continuous media; 1.3.3. Summary of the problem of small movements of an elastic continuous medium in adiabatic mode; 1.3.4. Position of static equilibrium of an elastic solid medium; 1.3.5. Vibrations of elastic solid media; 1.3.6. Boundary conditions; 1.3.7. Vibrations equations; 1.3.8. Notes on the initial conditions of the problem of vibrations; 1.3.9. Formulation in displacement; 1.3.10. Vibration of viscoelastic solid media; 1.4. Conclusion 327 $aChapter 2. Variational Formulation for Vibrations of Elastic Continuous Media2.1. Objective of the chapter; 2.2. Concept of the functional, bases of the variational method; 2.2.1. The problem; 2.2.2. Fundamental lemma; 2.2.3. Basis of variational formulation; 2.2.4. Directional derivative; 2.2.5. Extremum of a functional calculus; 2.3. Reissner's functional; 2.3.1. Basic functional; 2.3.2. Some particular cases of boundary conditions; 2.3.3. Case of boundary conditions effects of rigidity and mass; 2.4. Hamilton's functional; 2.4.1. The basic functional 327 $a2.4.2. Some particular cases of boundary conditions2.5. Approximate solutions; 2.6. Euler equations associated to the extremum of a functional; 2.6.1. Introduction and first example; 2.6.2. Second example: vibrations of plates; 2.6.3. Some results; 2.7. Conclusion; Chapter 3. Equation of Motion for Beams; 3.1. Objective of the chapter; 3.2. Hypotheses of condensation of straight beams; 3.3. Equations of longitudinal vibrations of straight beams; 3.3.1. Basic equations with mixed variables; 3.3.2. Equations with displacement variables 327 $a3.3.3. Equations with displacement variables obtained by Hamilton's functional3.4. Equations of vibrations of torsion of straight beams; 3.4.1. Basic equations with mixed variables; 3.4.2. Equation with displacements; 3.5. Equations of bending vibrations of straight beams; 3.5.1. Basic equations with mixed variables: Timoshenko's beam; 3.5.2. Equations with displacement variables: Timoshenko's beam; 3.5.3. Basic equations with mixed variables: Euler-Bernoulli beam; 3.5.4. Equations of the Euler-Bernoulli beam with displacement variable 327 $a3.6. Complex vibratory movements: sandwich beam with a flexible inside 330 $aThree aspects are developed in this book: modeling, a description of the phenomena and computation methods. A particular effort has been made to provide a clear understanding of the limits associated with each modeling approach. Examples of applications are used throughout the book to provide a better understanding of the material presented. 410 0$aISTE 606 $aVibration 606 $aContinuum mechanics 615 0$aVibration. 615 0$aContinuum mechanics. 676 $a531/.32 700 $aGuyader$b Jean-Louis$0912233 712 02$aSociete Francaise d'Acoustique. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911018949403321 996 $aVibration in continuous media$92042581 997 $aUNINA