Vibration of Functionally Graded Beams and Plates uses numerically efficient computational techniques to analyze vibration problems associated with FG beams and plates. Introductory material on FG materials and structural members, as well as a range of vibration and shear deformation theories are discussed, providing a valuable summary of these broader themes. The latest research and analysis of vibration in FG materials is presented in an application-oriented manner, linking the research to its importance in fields such as aerospace, nuclear power, and automotive engineering. The book also features research on the complicating effects of thermal environments, piezoelectricity, and elastic foundations. The innovative computational procedures and simulation results are shown in full throughout, providing a uniquely valuable resource for users of numerical modeling software. This book is essential reading for any researcher or practitioner interested in FG materials, or the design of technology for the nuclear power, aerospace, and automotive industries. - Defines the basic preliminaries of vibration and FG materials - Introduces historical background and recent developments in functionally graded materials with references for further reading - Shows computational procedures with simulation results - Includes many easy to understand example problems - Presents various analytical and numerical procedures for each solution

Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for beams and which has become established and recognised globally as the most important contribution to the field in the last quarter of a century. The Carrera Unified Formulation (CUF) has hierarchical properties, that is, the error can be reduced by increasing the number of the unknown variables. This formulation is extremely suitable for computer implementations and can deal with most typical engineering challenges. It overcomes the problem of classical formulae that require different formulas for tension, bending, shear and torsion; it can be applied to any beam geometries and loading conditions, reaching a high level of accuracy with low computational cost, and can tackle problems that in most cases are solved by employing plate/shell and 3D formulations. Key features: compares classical and modern approaches to beam theory, including classical well-known results related to Euler-Bernoulli and Timoshenko beam theories pays particular attention to typical applications related to bridge structures, aircraft wings, helicopters and propeller blades provides a number of numerical examples including typical Aerospace and Civil Engineering problems proposes many benchmark assessments to help the reader implement the CUF if they wish to do so accompanied by a companion website hosting dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given in the book as well as to solve other problems of their own www.mul2.com Researchers of continuum mechanics of solids and structures and structural analysts in industry will find this book extremely insightful. It will also be of great interest to graduate and postgraduate students of mechanical, civil and aerospace engineering.

Elastodynamics, Volume II: Linear Theory is a continuation of Volume I and discusses the dynamical theory of linear isotropic elasticity. The volume deals with the fundamental theorems regarding elastodynamics and the different mathematical methods of solution and their employment in one, two, and three dimensions. The text outlines the fundamentals of linear elastodynamics and explains basic equations, displacement formulation, stress formulation, and the uniqueness theorem of elastodynamics. The book also investigates elastodynamic problems involving one-space dimension in governing boundaries, equations, and initial conditions. The book then compares two-dimensional problems as being subject to more precise mathematical analysis compared to three-dimensional situations by using scalar wave equations. The text then analyzes elastodynamic problems in three space dimensions when the solution depends on the condition of separability of the vector wave equation and the satisfaction of the boundary conditions. The diffraction of elastic waves is also described using two approaches: the integral equation method or the Eigen function technique. The book can prove valuable to researchers and practitioners whose work involves advanced statistics, general physics, and thermodynamics.

The Functionally Graded Materials (FGM) concept originated in Japan in 1984 during the spaceplane project, in the form of a proposed thermal barrier material capable of withstanding a surface temperature of 2000 K and a temperature gradient of 1000 K across a cross section 10 mm. The materials can be designed for specific function and applications. FGMs offer great promise in applications where the operating conditions are extreme. For example, wear-resistant linings for handling large, heavy, abrasive ore particles; rocket heat shields; heat exchanger tubes; thermoelectric generators; heat-engine components; plasma facings for fusion reactors; and electrically insulating metal/ceramic joints. They are also ideal for minimizing thermomechanical mismatch in metal-ceramic bonding. This book is a result of contributions of experts from the international scientific community working in different aspects of functionally graded materials and structures and reports on the latest research and development findings on this topic through original and innovative research studies. Through its six chapters, the reader will have access to works related to processing, characteristics, modeling, and applications of functionally graded materials and structures.The book contains up-to-date publications from leading experts and the edition is intended to provide valuable recent information to the professionals involved in functionally graded materials and structure analysis and applications. The text is addressed not only to researchers, but also to professional engineers, students, and other experts in a variety of disciplines, both academic and industrial, seeking to gain a better understanding of what has been done in the field recently, and what open problems are in this area.

Encompassing formalism and structure in analytical dynamics, this graduate-level text discusses fundamentals of Newtonian and analytical mechanics, rigid body dynamics, problems in celestial mechanics and spacecraft dynamics, more. 1970 edition.

This unique book explores both theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates. It is ideal for researchers, professionals, students, and instructors. Expert researchers will find the most recent progresses in nonlinear vibrations and stability of shells and plates, including advanced problems of shells with fluid-structure interaction. Professionals will find many practical concepts, diagrams, and numerical results, useful for the design of shells and plates made of traditional and advanced materials. They will be able to understand complex phenomena such as dynamic instability, bifurcations, and chaos, without needing an extensive mathematical background. Graduate students will find (i) a complete text on nonlinear mechanics of shells and plates, collecting almost all the available theories in a simple form, (ii) an introduction to nonlinear dynamics, and (iii) the state of art on the nonlinear vibrations and stability of shells and plates, including fluid-structure interaction problems.

Mechanics of Functionally Graded Material Structures is an authoritative and fresh look at various functionally graded materials, customizing them with various structures. The book is devoted to tailoring material properties to the needed structural performance. The authors pair materials with the appropriate structures based upon their purpose and use.Material grading of structures depending upon thickness, axial and polar directions are discussed. Three dimensional analysis of rectangular plates made of functional graded materials and vibrational tailoring of inhomogeneous beams and circular plates are both covered in great detail. The authors derive novel closed form solutions that can serve as benchmarks that numerical solutions can be compared to. These are published for the first time in the literature. This is a unique book that gives the first exposition of the effects of various grading mechanisms on the structural behavior as well as taking into account vibrations and buckling.

Computational Structural Mechanics: Static and Dynamic Behaviors provides a cutting-edge treatment of functionally graded materials and the computational methods and solutions of FG static and vibration problems of plates. Using the Rayleigh-Ritz method, static and dynamic problems related to behavior of FG rectangular, Levy, elliptic, skew and annular plates are discussed in detail. A thorough review of the latest research results, computational methods and applications of FG technology make this an essential resource for researchers in academia and industry. - Explains application-oriented treatments of the functionally graded materials used in industry - Addresses relevant algorithms and key computational techniques - Provides numerical solutions of static and vibration problems associated with functionally graded beams and plates of different geometries

Seven years have elapsed since Dr. Renee Ford, editor-in-chief of Materials Technology, first suggested to me to publish a book on Functionally Graded Materials (FGMs). She said that the FGM concept, then largely unknown outside of Japan and a relatively few laboratories elsewhere, would be of great interest to everyone working in the materials field because of its potentially universal applicability. There was no book about FGMs in English at that time, although the number of research papers, review articles, and FGM conference proceedings had been increasing yearly. We discussed what the book should cover, and decided it should present a comprehensive description from basic theory to the most recent applications of FGMs. This would make it useful both as an introduction to FGMs for those simply curious about what this new materials field was all about, and also as a textbook for researchers, engineers, and graduate students in various material fields. The FGM Forum in Japan generously offered to support this publication program. is very difficult for an individual author to write a book that Because it covers such a wide range of various aspects of many different materials, I invited more than 30 eminent materials scientists throughout the world, who were associated with FGM research, to contribute selected topics. I also asked several leading researchers in this field to edit selected chapters: Dr. Barry H. Rabin, then at the U. S.

In general, every problem of science and engineering is governed by mathematical models. There is often a need to model, solve and interpret the problems one encounters in the world of practical problems. Models of practical application problems usually need to be handled by efficient computational models. New Paradigms in Computational Modeling and Its Applications deals with recent developments in mathematical methods, including theoretical models as well as applied science and engineering. The book focuses on subjects that can benefit from mathematical methods with concepts of simulation, waves, dynamics, uncertainty, machine intelligence, and applied mathematics. The authors bring together leading-edge research on mathematics combining various fields of science and engineering. This perspective acknowledges the inherent characteristic of current research on mathematics operating in parallel over different subject fields. New Paradigms in Computational Modeling and Its Applications meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of mathematics on the other. As such, the book contains 13 chapters covering various aspects of computational modeling from theoretical to application problems. The first six chapters address various problems of structural and fluid dynamics. The next four chapters include solving problems where the governing parameters are uncertain regarding fuzzy, interval, and affine. The final three chapters will be devoted to the use of machine intelligence in artificial neural networks. - Presents a self-contained and up to date review of modelling real life scientific and engineering application problems - Introduces new concepts of various computing techniques to handle different engineering and science problems - Demonstrates the efficiency and power of the various algorithms and models in a simple and easy to follow style, including numerous examples to illustrate concepts and algorithms