Vibrations of Elastic Systems

Solid Mechanics and Its Applications

Book 184
Springer Science & Business Media
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This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures.

Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated.

A large number of graphs and tables are given to show the impact of various factors on the systems’ natural frequencies, mode shapes, and responses.

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Additional Information

Publisher
Springer Science & Business Media
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Published on
Jan 12, 2012
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Pages
492
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ISBN
9789400726727
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Language
English
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Genres
Science / Mechanics / Dynamics
Science / Mechanics / General
Technology & Engineering / Manufacturing
Technology & Engineering / Mechanical
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Content Protection
This content is DRM protected.
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Recent developments in engineering and technology have brought about serious and enlarged demands for reliability, safety and economy in wide range of fields such as aeronautics, nuclear engineering, civil and structural engineering, automotive and production industry. This, in turn, has caused more interest in continuum damage mechanics and its engineering applications.

This book aims to give a concise overview of the current state of damage mechanics, and then to show the fascinating possibility of this promising branch of mechanics, and to provide researchers, engineers and graduate students with an intelligible and self-contained textbook.

The book consists of two parts and an appendix. Part I is concerned with the foundation of continuum damage mechanics. Basic concepts of material damage and the mechanical representation of damage state of various kinds are described in Chapters 1 and 2. In Chapters 3-5, irreversible thermodynamics, thermodynamic constitutive theory and its application to the modeling of the constitutive and the evolution equations of damaged materials are descried as a systematic basis for the subsequent development throughout the book.

Part II describes the application of the fundamental theories developed in Part I to typical damage and fracture problems encountered in various fields of the current engineering. Important engineering aspects of elastic-plastic or ductile damage, their damage mechanics modeling and their further refinement are first discussed in Chapter 6. Chapters 7 and 8 are concerned with the modeling of fatigue, creep, creep-fatigue and their engineering application. Damage mechanics modeling of complicated crack closure behavior in elastic-brittle and composite materials are discussed in Chapters 9 and 10. In Chapter 11, applicability of the local approach to fracture by means of damage mechanics and finite element method, and the ensuing mathematical and numerical problems are briefly discussed.

A proper understanding of the subject matter requires knowledge of tensor algebra and tensor calculus. At the end of this book, therefore, the foundations of tensor analysis are presented in the Appendix, especially for readers with insufficient mathematical background, but with keen interest in this exciting field of mechanics.

Free Mathematica 10 Update Included! Now available from www.wiley.com/go/magrab

Updated material includes:
- Creating regions and volumes of arbitrary shape and determining their properties: arc length, area, centroid, and area moment of inertia
- Performing integrations, solving equations, and determining the maximum and minimum values over regions of arbitrary shape
- Solving numerically a class of linear second order partial differential equations in regions of arbitrary shape using finite elements



An Engineer's Guide to Mathematica enables the reader to attain the skills to create Mathematica 9 programs that solve a wide range of engineering problems and that display the results with annotated graphics. This book can be used to learn Mathematica, as a companion to engineering texts, and also as a reference for obtaining numerical and symbolic solutions to a wide range of engineering topics. The material is presented in an engineering context and the creation of interactive graphics is emphasized.

The first part of the book introduces Mathematica's syntax and commands useful in solving engineering problems. Tables are used extensively to illustrate families of commands and the effects that different options have on their output. From these tables, one can easily determine which options will satisfy one's current needs. The order of the material is introduced so that the engineering applicability of the examples increases as one progresses through the chapters. The second part of the book obtains solutions to representative classes of problems in a wide range of engineering specialties. Here, the majority of the solutions are presented as interactive graphics so that the results can be explored parametrically.

Key features:

Material is based on Mathematica 9Presents over 85 examples on a wide range of engineering topics, including vibrations, controls, fluids, heat transfer, structures, statistics, engineering mathematics, and optimizationEach chapter contains a summary table of the Mathematica commands used for ease of referenceIncludes a table of applications summarizing all of the engineering examples presented.Accompanied by a website containing Mathematica notebooks of all the numbered examples

An Engineer's Guide to Mathematica is a must-have reference for practitioners, and graduate and undergraduate students who want to learn how to solve engineering problems with Mathematica.

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