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      1  Cover

      2  Title Page

      3  Copyright

      4  Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff

      5  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

      6  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

      7  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

      8  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

      9  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

      10  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

      11  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

      12  8 Nonlinear Dynamics and Phenomena in Oscillators with Hysteresis 8.1. Introduction СКАЧАТЬ