Modern Trends in Structural and Solid Mechanics 2 : Vibrations.

Intro -- Table of Contents -- Title Page -- Copyright -- Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff -- 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 -- List of Authors -- Index -- Summary of Volume 1 -- Summary of Volume 3.

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