Modern Trends in Structural and Solid Mechanics 2 Vibrations 1st Edition by Noël Challamel, Julius Kaplunov, Izuru Takewaki 1786307154 9781786307156
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ISBN 10: 1786307154
ISBN 13: 9781786307156
Author: Noël Challamel, Julius Kaplunov, Izuru Takewaki
This book – comprised of three separate volumes – presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This second volume is devoted to the vibrations of solid and structural members. Modern Trends in Structural and Solid Mechanics 2 has broad scope, covering topics such as: exact and approximate vibration solutions of rods, beams, membranes, plates and three-dimensional elasticity problems, Bolotin’s dynamic edge effect, the principles of plate theories in dynamics, nano- and microbeams, nonlinear dynamics of shear extensible beams, the vibration and aeroelastic stability behavior of cellular beams, the dynamic response of elastoplastic softening oscillators, the complex dynamics of hysteretic oscillators, bridging waves, and the three-dimensional propagation of waves. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.
Table of contents:
1 Bolotin’s Dynamic Edge Effect Method Revisited (Review)
1.1. Introduction
1.2. Toy problem: natural beam oscillations
1.3. Linear problems solved
1.4. Generalization for the nonlinear case
1.5. DEEM and variational approaches
1.6. Quasi-separation of variables and normal modes of nonlinear oscillations of continuous systems
1.7. Short-wave (high-frequency) asymptotics. Possible generalizations of DEEM
1.8. Conclusion: DEEM, highly recommended
1.9. Acknowledgments
1.10. Appendix
1.11. References
2 On the Principles to Derive Plate Theories
2.1. Introduction
2.2. Some historical remarks
2.3. Possibilities to formulate plate theories
2.4. Shear correction
2.5. Conclusion
2.6. References
3 A Softening–Hardening Nanomechanics Theory for the Static and Dynamic Analyses of Nanorods and Nanobeams: Doublet Mechanics
3.1. Introduction
3.2. Doublet mechanics formulation
3.3. Governing equations
3.4. Analytical solutions
3.5. Numerical results
3.6. Conclusion
3.7. References
4 Free Vibration of Micro-Beams and Frameworks Using the Dynamic Stiffness Method and Modified Couple Stress Theory
4.1. Introduction
4.2. Formulation of the potential and kinetic energies
4.3. Derivation of the governing differential equations
4.4. Development of the dynamic stiffness matrix
4.5. Application of the Wittrick–Williams algorithm
4.6. Numerical results and discussion
4.7. Conclusion
4.8. Acknowledgments
4.9. References
5 On the Geometric Nonlinearities in the Dynamics of a Planar Timoshenko Beam
5.1. Introduction
5.2. The geometrically exact planar Timoshenko beam
5.3. The asymptotic solution
5.4. The importance of nonlinear terms
5.5. Simplified models
5.6. Conclusion
5.7. References
6 Statics, Dynamics, Buckling and Aeroelastic Stability of Planar Cellular Beams
6.1. Introduction
6.2. Continuous models of planar cellular structures
6.3. The grid beam
6.4. Buckling
6.5. Dynamics
6.6. Aeroelastic stability
6.7. References
7 Collapse Limit of Structures under Impulsive Loading via Double Impulse Input Transformation
7.1. Introduction
7.2. Collapse limit corresponding to the critical timing of second impulse
7.3. Classification of collapse patterns in non-critical case
7.4. Analysis of collapse limit using energy balance law
7.5. Verification of proposed collapse limit via time-history response analysis
7.6. Conclusion
7.7. References
8 Nonlinear Dynamics and Phenomena in Oscillators with Hysteresis
8.1. Introduction
8.2. Hysteresis model and SDOF response to harmonic excitation
8.3. 2DOF hysteretic systems
8.4. Nonlinear modal interactions in 2DOF hysteretic systems
8.5. Conclusion
8.6. Acknowledgments
8.7. Appendix: Mechanical characteristics of SDOF and 2DOF systems
8.8. References
9 Bridging Waves on a Membrane: An Approach to Preserving Wave Patterns
9.1. Introduction
9.2. Problem statement
9.3. Homogenized bridge
9.4. Internal reflections
9.5. Discrete bridge
9.6. Net bridge
9.7. Concluding remarks
9.8. Acknowledgments
9.9. References
10 Dynamic Soil Stiffness of Foundations Supported by Layered Half-Space
10.1. Introduction
10.2. Generation of dynamic soil stiffness
10.3. Numerical examples of the generation of dynamic soil stiffness
10.4. Numerical examples of the generation of FRS
10.5. Conclusion
10.6. References
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