Modern Trends in Structural and Solid Mechanics 2

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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.
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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– “What more can be said about this monumental work, other than to express admiration? … The study is of great academic interest, and is clearly a labor of love. The author is to be congratulated on this work …” (Prof. H. D. Conway, Department of Theoretical and Applied Mechanics, Cornell University).

– “This book … is prepared by Isaac Elishakoff, one of the eminent solid mechanics experts of the 20th century and the present one, and his distinguished coauthors, will be of enormous use to researchers, graduate students and professionals in the fields of ocean, naval, aerospace and mechanical engineers as well as other fields” (Prof. Patricio A. A. Laura, Prof. Carlos A. Rossit, Prof. Diana V. Bambill, Universidad Nacional del Sur, Argentina, Ocean Engineering).

– “This book is an outstanding research monograph … extremely well written, informative, highly original … great scholarly contribution …. There is no comparable book discussing the combination of optimization and anti-optimization … magnificent monograph …. This book, which certainly is written with love and passion, is the first of its kind in applied mechanics literature, and has the potential of having a revolutionary impact on both uncertainty analysis and optimization” (Prof. Izuru Takewaki, Kyoto University, Engineering Structures).

– “This book is a collection of a surprisingly large number of closed form solutions, by the author and by others, involving the buckling of columns and beams, and the vibration of rods, beams and circular plates. The structures are, in general, inhomogeneous. Many solutions are published here for the first time. The text starts with an instructive review of direct, semi-inverse, and inverse eigenvalue problems. Unusual closed form solutions of column buckling are presented first, followed by closed form solutions of the vibrations of rods. Unusual closed form solutions for vibrating beams follow. The influence of boundary conditions on eigenvalues is discussed. An entire chapter is devoted to boundary conditions involving guided ends. Effects of axial loads and of elastic foundations are presented in two separate chapters. The closed form solutions of circular plates concentrate on axisymmetric vibrations. The scholarly effort that produced this book is remarkable” (Prof. Werner Soedel, then Editor-in-Chief of Journal Sound and Vibration).

– “The field has been brilliantly presented in book form …” (Prof. Luis A. Godoy et al., Institute of Advanced Studies in Engineering and Technology, Science Research Council of Argentina and National University of Cordoba, Argentina, Thin-Walled Structures).

– “Elishakoff is one of the pioneers in the use of the probabilistic approach for studying imperfection-sensitive structures” (Prof. Chiara Bisagni and Dr. Michela Alfano, Delft University of Technology; AIAA Journal).

– “Recently, Elishakoff et al. presented an excellent literature review on the historical development of Timoshenko’s beam theory” (Prof. Zhenlei Chen et al., Journal of Building Engineering).

Professor Isaac Elishakoff is the author or co-author of an impressive list of seminal books in the field of deterministic and non-deterministic mechanics, presented below.

Books by Elishakoff

Ben-Haim, Y. and Elishakoff, I. (1990). Convex Models of Uncertainty in Applied Mechanics . Elsevier, Amsterdam.

Cederbaum, G., Elishakoff, I., Aboudi, J., Librescu, L. (n.d.). Random Vibration and Reliability of Composite Structures . Technomic, Lancaster.

Elishakoff, I. (1983). Probabilistic Methods in the Theory of Structures . Wiley, New York.

Elishakoff, I. (1999). Probabilistic Theory of Structures . Dover Publications, New York.

Elishakoff, I. (2004). Safety Factors and Reliability: Friends or Foes? Kluwer Academic Publishers, Dordrecht.

Elishakoff, I. (2005). Eigenvalues of Inhomogeneous Structures: Unusual Closed-Form Solutions of Semi-Inverse Problems . CRC Press, Boca Raton.

Elishakoff, I. (2014). Resolution of the Twentieth Century Conundrum in Elastic Stability . World Scientific/Imperial College Press, Singapore.

Elishakoff, I. (2017). Probabilistic Methods in the Theory of Structures: Random Strength of Materials, Random Vibration, and Buckling . World Scientific, Singapore.

Elishakoff, I. (2018). Probabilistic Methods in the Theory of Structures: Solution Manual to Accompany Probabilistic Methods in the Theory of Structures: Problems with Complete, Worked Through Solutions . World Scientific, Singapore.

Elishakoff, I. (2020). Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells . Springer Nature, Switzerland.

Elishakoff, I. (2020). Handbook on Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories . World Scientific, Singapore.

Elishakoff, I. and Ohsaki, M. (2010). Optimization and Anti-Optimization of Structures under Uncertainty . Imperial College Press, London.

Elishakoff, I. and Ren, Y. (2003). Finite Element Methods for Structures with Large Stochastic Variations . Oxford University Press, Oxford.

Elishakoff, I., Lin, Y.K., Zhu, L.P. (1994). Probabilistic and Convex Modeling of Acoustically Excited Structures . Elsevier, Amsterdam.

Elishakoff, I., Li, Y., Starnes Jr., J.H. (2001). Non-Classical Problems in the Theory of Elastic Stability . Cambridge University Press, Cambridge.

Elishakoff, I., Pentaras, D., Dujat, K., Versaci, C., Muscolino, G., Storch, J., Bucas, S., Challamel, N., Natsuki, T., Zhang, Y., Ming Wang, C., Ghyselinck, G. (2012). Carbon Nanotubes and Nano Sensors: Vibrations, Buckling, and Ballistic Impact . ISTE Ltd, London, and John Wiley & Sons, New York.

Elishakoff, I., Pentaras, D., Gentilini, C., Cristina, G. (2015). Mechanics of Functionally Graded Material Structures . World Scientific/Imperial College Press, Singapore.

Books edited or co-edited by Elishakoff

Ariaratnam, S.T., Schuëller, G.I., Elishakoff, I. (1988). Stochastic Structural Dynamics – Progress in Theory and Applications . Elsevier, London.

Casciati, F., Elishakoff, I., Roberts, J.B. (1990). Nonlinear Structural Systems under Random Conditions . Elsevier, Amsterdam.

Chuh, M., Wolfe, H.F., Elishakoff, I. (1989). Vibration and Behavior of Composite Structures . ASME Press, New York.

David, H. and Elishakoff, I. (1990). Impact and Buckling of Structures . ASME Press, New York.

Elishakoff, I. (1999). Whys and Hows in Uncertainty Modeling . Springer, Vienna.

Elishakoff, I. (2007). Mechanical Vibration: Where Do We Stand? Springer, Vienna.

Elishakoff, I. and Horst, I. (1987). Refined Dynamical Theories of Beams, Plates and Shells and Their Applications . Springer Verlag, Berlin.

Elishakoff, I. and Lin, Y.K. (1991). Stochastic Structural Dynamics 2 – New Applications . Springer, Berlin.

Elishakoff, I. and Lyon, R.H. (1986), Random Vibration-Status and Recent Developments . Elsevier, Amsterdam.

Elishakoff, I. and Seyranian, A.P. (2002). Modern Problems of Structural Stability . Springer, Vienna.

Elishakoff, I. and Soize, C. (2012). Non-Deterministic Mechanics . Springer, Vienna.

Elishakoff, I., Arbocz, J., Babcock Jr., C.D., Libai, A. (1988). Buckling of Structures: Theory and Experiment . Elsevier, Amsterdam.

Lin, Y.K. and Elishakoff, I. (1991). Stochastic Structural Dynamics 1 – New Theoretical Developments . Springer, Berlin.

Noor, A.K., Elishakoff, I., Hulbert, G. (1990). Symbolic Computations and Their Impact on Mechanics . ASME Press, New York.

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