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This book presents in detail an alternative approach to solving problems involving both linear and nonlinear oscillations of elastic distributed parameter systems. It includes the so-called variational, projection and iterative gradient methods, which, when applied to nonlinear problems, use the procedure of linearization of the original non-linear equations. These methods are not universal and require a different solution for each problem or class of problems.However, in many cases the combination of the methods shown in this book leads to more efficient algorithms for solving important applied problems.To record these algorithms in a unified form, the first part of the book and its appendix devote considerable attention to compiling the general operator equations, which include (as particular cases) equations for vibrations in rods, plates, shells and three-dimensional bodies. They are mainly considered to be periodic or nearly periodic oscillations, which correspond to stationary or nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications. .
Engineering. --- Computer mathematics. --- Continuum mechanics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Vibration, Dynamical Systems, Control. --- Computational Science and Engineering. --- Continuum Mechanics and Mechanics of Materials. --- Elasticity --- Mathematics. --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties --- Computer science. --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Cycles --- Mechanics --- Sound --- Informatics --- Science --- Computer mathematics --- Electronic data processing --- Mathematics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy
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This book presents a modern and unconventional introduction to anisotropy. The first part presents a general description of Anisotropic Elasticity theories while the second part focuses on the polar formalism: the theoretical bases and results are completely developed along with applications to design problems of laminated anisotropic structures. The book is based on lectures on anisotropy which have been held at Ecole Polytechnique in Paris.
Composite materials --- Elasticity. --- Anisotropy. --- Mechanical properties. --- Anisotropic crystals --- Elastic properties --- Young's modulus --- Engineering. --- Continuum mechanics. --- Materials science. --- Continuum Mechanics and Mechanics of Materials. --- Characterization and Evaluation of Materials. --- Classical Mechanics. --- Crystallography --- Matter --- Mathematical physics --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties --- Mechanics. --- Mechanics, Applied. --- Surfaces (Physics). --- Solid Mechanics. --- Physics --- Surface chemistry --- Surfaces (Technology) --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Material science --- Physical sciences --- Solids. --- Materials --- Characterization and Analytical Technique. --- Analysis. --- Solid state physics --- Transparent solids
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