
Modern Trends in Structural and Solid Mechanics 2
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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.
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Persons
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.
Content
- 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
- End User License Agreement
Preface
Short Bibliographical Presentation of Prof. Isaac Elishakoff
This book is dedicated to Prof. Isaac Elishakoff by his colleagues, friends and former students, on the occasion of his seventy-fifth birthday.
Figure P.1. Prof. Isaac Elishakoff
Prof. Isaac Elishakoff is an international leading authority across a broad area of structural mechanics, including dynamics and stability, optimization and anti-optimization, probabilistic methods, analysis of structures with uncertainty, refined theories, functionally graded material structures, and nanostructures. He was born in Kutaisi, Republic of Georgia, on February 9, 1944.
Figure P.2. Elishakoff in middle school in the city of Sukhumi, Georgia
Elishakoff holds a PhD in Dynamics and Strength of Machines from the Power Engineering Institute and Technical University in Moscow, Russia (Figure P.4 depicts the PhD defense of Prof. Isaac Elishakoff).
Figure P.3. Elishakoff just before acceptance to university. Photo taken in Sukhumi, Georgia
Figure P.4. Public PhD defense, Moscow Power Engineering Institute and State University; topic "Vibrational and Acoustical Fields in the Circular Cylindrical Shells Excited by Random Loadings", and dedicated to the evaluation of noise levels in TU-144 supersonic aircraft
His supervisor was Prof. V. V. Bolotin (1926-2008), a member of the Russian Academy of Sciences (Figure P.5 shows Elishakoff with Bolotin some years later).
Figure P.5. Elishakoff with Bolotin (middle), member of the Russian Academy of Sciences, and Prof. Yukweng (Mike) Lin (left), member of the US National Academy of Engineering. Photo taken at Florida Atlantic University during a visit from Bolotin
Currently, Elishakoff is a Distinguished Research Professor in the Department of Ocean and Mechanical Engineering at Florida Atlantic University. Before joining the university, he taught for one year at Abkhazian University, Sukhumi in the Republic of Georgia, and 18 years at the Technion - Israel Institute of Technology in Haifa, where he became the youngest full professor at the time of his promotion (Figure P.6 shows Elishakoff presenting a book to Prof. Josef Singer, Technion's former president).
Figure P.6. Prof. Elishakoff presenting a book to Prof. J. Singer, Technion's President; right: Prof. A. Libai, Aerospace Engineering Department, Technion
Elishakoff has lectured at about 200 meetings and seminars, including about 60 invited, plenary or keynote lectures, across Europe, North and South America, the Middle East and the Far East.
Prof. Elishakoff has made vital and outstanding contributions in a number of areas in structural mechanics. In particular, he has analyzed random vibrations of homogeneous and composite beams, plates and shells, with special emphasis on the effects of refinements in structural theories and cross-correlations. Free structural vibrations have been tackled using a non-trivial generalization of Bolotin's dynamic edge effect method. Nonlinear buckling has been investigated using a novel method, incorporating experimental analysis of imperfections. As a result, the fundamental concept of closing the gap - spanning the entire 20th century - between theory and practice in imperfection-sensitive structures has been proposed. Novel methods of evaluating structural reliability have been proposed, taking into account the error associated with various low-order approximations, as well as human error; innovative generalization of the stochastic linearization method has been advanced. A non-probabilistic theory for treating uncertainty in structural mechanics has been established. Dynamic stability of elastic and viscoelastic structures with imperfections has been studied. An improved, non-perturbative stochastic finite element method for structures has been developed. The list of Elishakoff's remarkable research achievements goes on.
His research has been acknowledged by many awards and prizes. He is a member of the European Academy of Sciences and Arts, a Fellow of the American Academy of Mechanics and ASME, and a Foreign Member of the Georgian National Academy of Sciences. Elishakoff is also a recipient of the Bathsheva de Rothschild prize (1973) and the Worcester Reed Warner Medal of the American Society of Mechanical Engineers (2016).
Figure P.7. Elishakoff having received the William B. Johnson Inter- Professional Founders Award
Elishakoff is directly involved in numerous editorial activities. He serves as the book review editor of the "Journal of Shock and Vibration" and is currently, or has previously been an associate editor of the International Journal of Mechanics of Machines and Structures, Applied Mechanics Reviews, and Chaos, Solitons & Fractals. In addition, he is or has been on the editorial boards of numerous journals, for example Journal of Sound and Vibration, International Journal of Structural Stability and Dynamics, International Applied Mechanics and Computers & Structures. He also acts as a book series editor for Elsevier, Springer and Wiley.
Figure P.8. Inauguration as the Frank Freimann Visiting Professor of Aerospace and Mechanical Engineering; left: Rev. Theodore M. Hesburgh, President of the University of Notre Dame; right: Prof. Timothy O'Meara, Provost
Prof. Elishakoff has held prestigious visiting positions at top universities all over the world. Among them are Stanford University (S. P. Timoshenko Scholar); University of Notre Dame, USA (Frank M. Freimann Chair Professorship of Aerospace and Mechanical Engineering and Henry J. Massman, Jr. Chair Professorship of Civil Engineering); University of Palermo, Italy (Visiting Castigliano Distinguished Professor); Delft University of Technology, Netherlands (multiple appointments, including the W. T. Koiter Chair Professorship of the Mechanical Engineering Department - see Figure P.9); Universities of Tokyo and Kyoto, Japan (Fellow of the Japan Society for the Promotion of Science); Beijing University of Aeronautics and Astronautics, People's Republic of China (Visiting Eminent Scholar); Technion, Haifa, Israel (Visiting Distinguished Professor); University of Southampton, UK (Distinguished Visiting Fellow of the Royal Academy of Engineering).
Figure P.9. Prof. Elishakoff with Prof. Warner Tjardus Koiter, Delft University of Technology (center), and Dr. V. Grishchak, of Ukraine (right)
Figure P.10. Elishakoff and his colleagues during the AIAA SDM Conference at Palm Springs, California in 2004; Standing, from right to left, are Prof. Elishakoff, the late Prof. Josef Singer and Dr. Giora Maymon of RAFAEL. Sitting is the late Prof. Avinoam Libai
Elishakoff has made a substantial contribution to conference organization. In particular, he participated in the organization of the Euro-Mech Colloquium on "Refined Dynamical Theories of Beams, Plates and Shells, and Their Applications" in Kassel, Germany (1986); the Second International Conference on Stochastic Structural Dynamics, in Boca Raton, USA (1990); "International Conference on Uncertain Structures" in Miami, USA and Western Caribbean (1996). He also coordinated four special courses at the International Centre for Mechanical Sciences (CISM), in Udine, Italy (1997, 2001, 2005, 2011).
Prof. Elishakoff has published over 540 original papers in leading journals and conference proceedings. He championed authoring, co-authoring or editing of 31 influential and extremely well-received books and edited volumes.
Here follows some praise of his work and books:
- - "It was not until 1979, when Elishakoff published his reliability study . that a method has been proposed, which made it possible to introduce the results of imperfection surveys . into the analysis ." (Prof. Johann Arbocz, Delft University of Technology, The Netherlands, Zeitschrift für Flugwissenschaften und Weltraumforschung).
- - "He has achieved world renown . His research is characterized by its originality and a combination of mathematical maturity and physical understanding which is reminiscent of von Kármán ." (Prof. Charles W. Bert, University of Oklahoma).
- - "It is clear that Elishakoff is a world leader in his field . His outstanding reputation is very well deserved ." (Prof. Bernard Budiansky, Harvard University).
- - "Professor Isaac Elishakoff . is subject-wise very much an all-round vibrationalist" (P. E. Doak, Editor in Chief, Journal of Sound and Vibration, University of Southampton, UK).
- - "This is a beautiful book ." (Dr. Stephen H. Crandall, Ford Professor of Engineering, M.I.T.).
- - "Das Buch ist in seiner Aufmachunghervorragendgestaltet und kannalsäusserstwertvolleErganzung . wäzmstensempfohlenwerden ." [The book's appearance is perfectly designed and can be highly recommended as a valuable...
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