(Ebook) Vibration in Continuous Media 1st Edition by Jean Louis Guyader ISBN 9781905209279 1905209274

(Ebook) Vibration in Continuous Media 1st Edition by Jean Louis Guyader ISBN 9781905209279 1905209274

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ISBN 10: 1905209274
ISBN 13: 9781905209279
Author: Jean Louis Guyader

(Ebook) Vibration in Continuous Media 1st Edition Table of contents:

Chapter 1: Vibrations of Continuous Elastic Solid Media
1.1 Objective of the chapter
1.2 Equations of motion and boundary conditions of continuous media
1.3 Study of the vibrations: small movements around a position of static, stable equilibrium
1.4 Conclusion

Chapter 2: Variational Formulation for Vibrations of Elastic Continuous Media
2.1 Objective of the chapter
2.2 Concept of the functional, bases of the variational method
2.3 Reissner’s functional
2.4 Hamilton’s functional
2.5 Approximate solutions
2.6 Euler equations associated with the extremum of a functional
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
3.4 Equations of torsional vibrations of straight beams
3.5 Equations of bending vibrations of straight beams
3.6 Complex vibratory movements: sandwich beam with a flexible inside
3.7 Conclusion

Chapter 4: Equation of Vibration for Plates
4.1 Objective of the chapter
4.2 Thin plate hypotheses
4.3 Equations of motion and boundary conditions of in‑plane vibrations
4.4 Equations of motion and boundary conditions of transverse vibrations
4.5 Coupled movements
4.6 Equations with polar coordinates
4.7 Conclusion

Chapter 5: Vibratory Phenomena Described by the Wave Equation
5.1 Introduction
5.2 Wave equation: presentation and uniqueness of the solution
5.3 Solution via propagation method (d’Alembert’s method)
5.4 Solution via separation of variables
5.5 Applications
5.6 Conclusion

Chapter 6: Free Bending Vibration of Beams
6.1 Introduction
6.2 The problem
6.3 Solution for homogeneous beam with constant cross‑section
6.4 Propagation in infinite beams
6.5 Introduction of boundary conditions: vibration modes
6.6 Stress‑displacement relationship
6.7 Influence of secondary effects
6.8 Conclusion

Chapter 7: Bending Vibration of Plates
7.1 Introduction
7.2 Setting up the problem: writing boundary conditions
7.3 Solution of equation via separation of variables
7.4 Vibration modes of plates supported at two opposite edges
7.5 Vibration modes of rectangular plates: approximation by edge‑effect method
7.6 Calculation of free vibratory response following initial conditions
7.7 Circular plates
7.8 Conclusion

Chapter 8: Introduction to Damping: Example of the Wave Equation
8.1 Introduction
8.2 Wave equation with viscous damping
8.3 Damping via dissipative boundary conditions
8.4 Viscoelastic beam
8.5 Orthogonality properties of damped systems
8.6 Conclusion

Chapter 9: Calculation of Forced Vibrations by Modal Expansion
9.1 Objective of the chapter
9.2 Steps for calculating response via modal decomposition
9.3 Examples: generalized mass and stiffness
9.4 Solution of modal equation
9.5 Example of response calculation
9.6 Convergence of modal series
9.7 Conclusion

Chapter 10: Calculation of Forced Vibrations by Forced Wave Decomposition
10.1 Introduction
10.2 Method illustrated with torsional vibration of a beam
10.3 Resolution of bending problems
10.4 Damped media (longitudinal beam vibrations)
10.5 Generalization: distributed excitations and non‑harmonic excitations
10.6 Forced vibrations of rectangular plates
10.7 Conclusion

Chapter 11: The Rayleigh‑Ritz Method based on Reissner’s Functional
11.1 Introduction
11.2 Variational formulation for bending vibrations of beams
11.3 Generation of functional spaces
11.4 Approximation of the vibratory response
11.5 Method formulation
11.6 Application to a clamped‑free beam
11.7 Conclusion

Chapter 12: The Rayleigh‑Ritz Method based on Hamilton’s Functional
12.1 Introduction
12.2 Reference example: bending vibrations of beams
12.3 Finite-element–type functional basis: applied to longitudinal beam vibrations
12.4 Modal-type functional basis: applied to plates with heterogeneities
12.5 Elastic boundary conditions
12.6 Convergence of Rayleigh‑Ritz method
12.7 Conclusion

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Tags: Jean Louis Guyader, Vibration, Continuous Media