Modern Trends in Structural and Solid Mechanics 2

Nöel Challamel is Professor at the University of Southern Brittany, France. He is the co-author of several books and over a hundred journal papers in the field of mechanics and civil engineering and is on the editorial board of numerous international journals. He is also Editor and Head of the Solid Mechanics and Mechanical Engineering series published by ISTE-Wiley.Julius Kaplunov is Professor at Keele University, UK. He is the co-author of over a hundred publications in mechanics, including three books. He is a member of the European Academy of Sciences and sits on the editorial boards of more than ten journals.Izuru Takewaki is Professor of building structures at Kyoto University, Japan, and is the 56th President of the Architectural Institute of Japan. He is the Field Chief Editor of Frontiers in Built Environment and has published over 200 international journal papers.

• Preface xiNoël CHALLAMEL, Julius KAPLUNOV and Izuru TAKEWAKIChapter 1. Bolotin’s Dynamic Edge Effect Method Revisited (Review) 1Igor V. ANDRIANOV and Lelya A. KHAJIYEVA1.1. Introduction 11.2. Toy problem: natural beam oscillations 21.3. Linear problems solved 61.4. Generalization for the nonlinear case 81.5. DEEM and variational approaches 121.6. Quasi-separation of variables and normal modes of nonlinear oscillations of continuous systems 161.7. Short-wave (high-frequency) asymptotics. Possible generalizations of DEEM 171.8. Conclusion: DEEM, highly recommended 191.9. Acknowledgments 201.10. Appendix 201.11. References 21Chapter 2. On the Principles to Derive Plate Theories 29Marcus AßMUS and Holm ALTENBACH2.1. Introduction 292.2. Some historical remarks 302.3. Possibilities to formulate plate theories 312.3.1. Theories based on hypotheses 322.3.2. Reduction of the governing equations by mathematical techniques 332.3.3. Direct approach 342.3.4. Consistent approach 362.4. Shear correction 362.5. Conclusion 382.6. References 39Chapter 3. A Softening–Hardening Nanomechanics Theory for the Static and Dynamic Analyses of Nanorods and Nanobeams: Doublet Mechanics 43Ufuk GUL and Metin AYDOGDU3.1. Introduction 433.2. Doublet mechanics formulation 463.3. Governing equations 493.3.1. Static equilibrium equations of a nanorod with periodic micro- and nanostructures 493.3.2. Equations of motion of a nanorod with periodic micro- and nanostructures 513.3.3. Static equilibrium equations of a nanobeam with periodic micro- and nanostructures 533.3.4. Equations of motion of a nanobeam with periodic micro- and nanostructures 553.4. Analytical solutions 563.4.1. Axial deformation of nanorods with periodic nanostructures 563.4.2. Vibration analysis of nanorods with periodic nanostructures 573.4.3. Axial wave propagation in nanorods with periodic nanostructures 583.4.4. Flexural deformation of nanobeams with periodic nanostructures 593.4.5. Buckling analysis of nanobeams with periodic nanostructures 603.4.6. Vibration analysis of nanobeams with periodic nanostructures 603.4.7. Flexural wave propagation in nanobeams with periodic nanostructures 613.5. Numerical results 623.6. Conclusion 753.7. References 76Chapter 4. Free Vibration of Micro-Beams and Frameworks Using the Dynamic Stiffness Method and Modified Couple Stress Theory 79J.R. BANERJEE4.1. Introduction 804.2. Formulation of the potential and kinetic energies 834.3. Derivation of the governing differential equations 864.4. Development of the dynamic stiffness matrix 884.4.1. Axial stiffnesses 894.4.2. Bending stiffnesses 904.4.3. Combination of axial and bending stiffnesses 924.4.4. Transformation matrix 934.5. Application of the Wittrick–Williams algorithm 944.6. Numerical results and discussion 954.7. Conclusion 1044.8. Acknowledgments 1044.9. References 104Chapter 5. On the Geometric Nonlinearities in the Dynamics of a Planar Timoshenko Beam 109Stefano LENCI and Giuseppe REGA5.1. Introduction 1095.2. The geometrically exact planar Timoshenko beam 1145.3. The asymptotic solution 1175.4. The importance of nonlinear terms 1195.4.1. An initial case 1195.4.2. The effect of the slenderness 1265.4.3. The effect of the end spring 1305.4.4. The effect of the resonance order 1315.5. Simplified models 1345.5.1. Neglecting axial inertia 1355.5.2. One-field equation 1365.5.3. The Euler–Bernoulli nonlinear beam 1385.6. Conclusion 1395.7. References 140Chapter 6. Statics, Dynamics, Buckling and Aeroelastic Stability of Planar Cellular Beams 143Angelo LUONGO6.1. Introduction 1436.2. Continuous models of planar cellular structures 1456.2.1. Timoshenko beam 1456.2.2. Shear beam 1476.2.3. Elastic constant identification 1486.3. The grid beam 1496.3.1. Rigid transverse model 1506.3.2. Flexible transverse model 1516.3.3. Comparison among models 1526.4. Buckling 1546.4.1. Formulation 1546.4.2. Critical loads 1566.5. Dynamics 1586.5.1. Timoshenko beam 1586.5.2. Shear beam and discrete spring–mass model 1596.6. Aeroelastic stability 1606.6.1. Modeling a base-isolated tower 1606.6.2. Critical wind velocity 1626.7. References 163Chapter 7. Collapse Limit of Structures under Impulsive Loading via Double Impulse Input Transformation 167Izuru TAKEWAKI, Kotaro KOJIMA and Sae HOMMA7.1. Introduction 1677.2. Collapse limit corresponding to the critical timing of second impulse 1717.3. Classification of collapse patterns in non-critical case 1757.4. Analysis of collapse limit using energy balance law 1777.4.1. Collapse Pattern 1’ 1777.4.2. Collapse Pattern 2’ 1787.4.3. Collapse Pattern 3’ 1797.4.4. Collapse Pattern 4’ 1797.5. Verification of proposed collapse limit via time-history response analysis 1817.6. Conclusion 1827.7. References 183Chapter 8. Nonlinear Dynamics and Phenomena in Oscillators with Hysteresis 185Fabrizio VESTRONI and Paolo CASINI8.1. Introduction 1868.2. Hysteresis model and SDOF response to harmonic excitation 1878.3. 2DOF hysteretic systems 1908.3.1. Equations of motion 1918.3.2. Modal characteristics 1928.4. Nonlinear modal interactions in 2DOF hysteretic systems 1928.4.1. Top-hysteresis configuration (TC) 1928.4.2. Base-hysteresis configuration (BC) 1958.5. Conclusion 1988.6. Acknowledgments 1998.7. Appendix: Mechanical characteristics of SDOF and 2DOF systems 1998.8. References 200Chapter 9. Bridging Waves on a Membrane: An Approach to Preserving Wave Patterns 203Peter WOOTTON and Julius KAPLUNOV9.1. Introduction 2039.2. Problem statement 2059.3. Homogenized bridge 2099.4. Internal reflections 2139.5. Discrete bridge 2179.6. Net bridge 2229.7. Concluding remarks 2269.8. Acknowledgments 2279.9. References 227Chapter 10. Dynamic Soil Stiffness of Foundations Supported by Layered Half-Space 231Yang ZHOU and Wei-Chau XIE10.1. Introduction 23110.2. Generation of dynamic soil stiffness 23310.2.1. Dynamic stiffness matrix under point loads 23310.2.2. Formulation of the flexibility function 23610.2.3. Formulation of Green’s influence function 23710.2.4. Total dynamic soil stiffness by the boundary element method 23910.3. Numerical examples of the generation of dynamic soil stiffness 24210.3.1. A rigid square foundation supported by a layer on half-space 24310.3.2. A rigid circular foundation supported by a layer on half-space 24410.3.3. A rigid circular foundation supported by half-space and a layer on half-space 24410.4. Numerical examples of the generation of FRS 24510.5. Conclusion 25010.6. References 250List of Authors 253Index 255Summaries of Volumes 1 and 3 257