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Journal of Sound and Vibration

Journal of Sound and Vibration 332 (2013) 6537–6538

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journal homepage: www.elsevier.com/locate/jsvi

Book Review

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling, Walter Lacarbonara. Springer (2013).819 pp., US$279.00, ISBN-10: 1441912754, ISBN-13: 978-1441912756.

This book has been written by an international authority in the field of nonlinear mechanics and offers one of the mostcomprehensive unifications of the foundations of nonlinear structural mechanics with practical engineering to emerge inrecent years. The book covers the modelling and computation of virtually all the necessary structural elements requiredby the nonlinear mechanician, and also offers precise and considered summaries of the mechanical phenomenology to beseen in such elements when considered in isolation and also when incorporated into real engineering structures. It isthis integration of beautifully presented theories with real engineering mechanics which makes this such a unique andwelcome book.

The book comprises eleven chapters each of which concludes in a set of questions, and many detailed and illuminatingsolutions are provided at the end. Four hundred and eighty eight references are included, and a key feature of this book isthe attention that has been paid to the use of the experimental data wherever possible throughout the book to verifytheoretical results. A further aspect is the prominence of stability and bifurcation theory in the second chapter with acorrespondingly clear statement of the terminology from first principles.

The first chapter starts by defining concepts, methods, and paradigms, looking at linearity and nonlinearity and applyingthe ubiquitous pendulum problem as a physically assimilable basis for understanding deep and subtle nonlinear phenomena.Exceptional attention to notational detail is evident, rendering a clear yet thorough definition throughout. The relevanceof higher order terms as indicators of loss of the linearised equilibrium condition due to finite configurational changes ishighlighted, and then computational strategies for step-by-step solution are outlined in rigorous detail. This leads into asection on the state-space formulation and the rôle of the Poincaré map. An excellent example is given of a single degree offreedom electrostatically forced MEMS micro-beam. The first chapter ends with various examples of path-following of limitcycles and periodic solutions, in the form of nonlinearly viscoelastic structures, shape memory oscillators, flutter control ofan aerofoil, an aeroelastic hysteretic vibration absorber, and the Bouc–Wen hysteresis model.

Chapter 2 is entitled ‘Stability and bifurcation of structures’ and special attention is paid to flutter, galloping, andMathieu-type instability in a range of structural elements and structures. The chapter goes on to treat equilibrium states andthen the stability of conservative and non-conservative systems and structures, and static bifurcations of conservativestructures, with useful engineering examples. Buckling and dynamic bifurcations within flutter and parametric resonanceproblems lead into a very interesting treatment of multi-pendulum systems, and the concept of internal energy transferbetween sub-elements through autoparametric interaction. The chapter finishes with the parametric resonance of sphericaland cylindrical shells under pulsating pressures. The third chapter concentrates entirely on the nonlinear problems inherentin elastic strings and cables, going fromwire ropes through to momentum exchange space tethers. The theoretical treatmentis consistently rigorous, dealing with the one dimensional string model and inclined cables, and then introducing theGalerkin model for the incremental cable problemwhen subject to planar forces. An excellent and challenging developmentensues in the form of a suspension bridge construction leading naturally to a discussion of the dynamics of sagging cables.A final short section explains fundamental aspects of the momentum exchange tether and there is also a useful mention ofthe electrodynamic tether variant. Finally there is the most interesting and thorough appendix provided which gives a casestudy on the bifurcations for the galloping of iced cables subject to steady winds. In chapter 4 the approach changes a littleso that the full formal theory for the nonlinear mechanics of three-dimensional solids can be explained in a logical andprocedural manner. The material in this chapter tackles this major area from both the material and spatial perspectives,leading to a statement for the stretch tensor by means of a full and rigorous application of the theory of deformation. Stresstheory analysis builds up to a formal statement of the stress tensor from which the procedure for obtaining the equationsof motion is elucidated in practice, in a precise step-by-step manner. Then the constitutive equations, material isotropyconditions, and compressibility and non-compressibility issues are all presented sequentially, culminating in a practicalstrain gauge example within which important aspects of the theory are applied. Two appendices are provided at the end, thefirst summarising energy and thermodynamic effects, and the second offering a concise statement of the curvilinear

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Book Review / Journal of Sound and Vibration 332 (2013) 6537–65386538

coordinates. The full nonlinear theory for beams is elucidated in the most systematic way possible in the fifth chapter,starting with beams undergoing planar motion, and proceeding from there to an exposition of beams in space. Equations ofmotion in space are obtained, with an interesting digression in which special Cosserat theory is compared with nonlinearthree-dimensional theory. The final section covers rotating beams in space. Two appendices round the chapter off with asummary treatment of the space and time differentiation of moving frames, and the parameterisation of rotations in space.Chapter 6 treats elastic instabilities of slender structures and covers frames and aircraft wings. The flutter Hopf bifurcationof nonlinear wings subject to steady air flows rounds this chapter off. An interesting section on the buckling of open thin-walled beams is included, with important examples given for real structural sections. A wealth of practically useful analysisis provided for the engineering analyst within this chapter. The next chapter covers a full nonlinear treatment of the theoryof curved beams and flexurally stiff cables, with a discussion of numerous structural examples. The treatment of flexurallystiff cables applies equally to applications to aerospace systems, tethers, and mooring cables. Chapter 8 is given up entirelyto the nonlinear theory of plates, including multi-layered laminate plates. Experimental results for multi-layered compositeplates are also quoted. Both buckling and vibration problems are treated here, and the theoretical discussion also usefullyextends to the buckling of thick plates. Applications are covered in chapter 9, and integration of the beams, plates, cables,and arches of previous chapters is the main thrust here. There is particular emphasis given to cable supported structuressuch as suspension bridges. This leads to an analysis of suspension bridges undergoing planar motion, and planar equili-brium and dynamic responses are discussed in detail. Cable stayed and guyed structures complete this presentation of richand interesting applications. The penultimate chapter continues the application theme, with the focus on the nonlineartheory of cable-supported structures, and with a fascinating case study of the arched Ponte della Musica over the river Tiberin Rome. The book concludes with a chapter on discretisation methods, treating the discretisation of distributed parametersystems, the method of weighted residuals – and its statement for dynamic problems, the Galerkin and Ritz methods, andfinishing with a nonlinear finite element formulation for continuation analysis.

This book is a really exceptional treatise of the highest quality and utility and stands out as a superb unification oftheoretical rigour and engineering application. I recommend it without reservation to students, researchers, and academicfaculty at every level who wish to really understand the theories of nonlinear mechanics and then to apply them to realproblems in engineering.

Matthew P. CartmellDepartment of Mechanical Engineering, University of Sheffield, Sheffield, UK

E-mail address: M.Cartmell@sheffield.ac.uk

Available online 20 August 2013