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eBook: ISBN:  9781470439170 
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AMS Member Price:  $122.40 
Softcover ISBN:  9780821869932 
Product Code:  CRMP/3 
List Price:  $104.00 
MAA Member Price:  $93.60 
AMS Member Price:  $83.20 
eBook ISBN:  9781470439170 
Product Code:  CRMP/3.E 
List Price:  $98.00 
MAA Member Price:  $88.20 
AMS Member Price:  $78.40 
Print ISBN:  
eBook ISBN:  9781470439170 
Product Code:  CRMP/3.B 
List Price:  $153.00 
MAA Member Price:  $137.70 
AMS Member Price:  $122.40 

Book DetailsCRM Proceedings & Lecture NotesVolume: 3; 1993; 282 ppMSC: Primary 34; Secondary 35
Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
ReadershipMathematics, physics, and engineering advanced undergraduates and graduate students in a course on asymptotic methods and solid mechanics. Scientists and engineers interested in the application of asymptotic methods to problems of mechanics and buckling and vibrations of thin structures.

Table of Contents

Part 1. A Survey

Asymptotic methods in mechanics with applications to thin shells and plates (introduction)

Chapter 1. Asymptotic expansions

Chapter 2. Singular perturbation of linear differential equations

Chapter 3. Degenerate boundary value problems

Chapter 4. Asymptotic solutions of partial differential equations

Chapter 5. Asymptotic solutions of nonlinear differential equations

References

Part 2. Thirteen Papers

Perturbation methods in eddy current testing

Buckling of thin cylindrical shells and shells of negative Gaussian curvature

Thermoelastic deformations of mirrors

A mathematical model for hydroelastic problems with a fluid memory. Part I

A mathematical model for hydroelastic problems with a fluid memory. Part II

Lowfrequency vibrations of cylindrical shells. Part I: Shells with a slanted edge

Lowfrequency vibrations of cylindrical shells. Part II: Connected shells

Buckling of convex shells under nonaxisymmetric loading

Elastoplastic deformations of ribbed plates

Elastic wave propagation through elastic shells

Dynmamic stability and forced vibrations of a horizontal rotor with a cracked shaft

Edge effect under large axisymmetric deformations of shells of revolution

Turning points and caustics in linear problems of thin shell free vibrations and buckling


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Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
Mathematics, physics, and engineering advanced undergraduates and graduate students in a course on asymptotic methods and solid mechanics. Scientists and engineers interested in the application of asymptotic methods to problems of mechanics and buckling and vibrations of thin structures.

Part 1. A Survey

Asymptotic methods in mechanics with applications to thin shells and plates (introduction)

Chapter 1. Asymptotic expansions

Chapter 2. Singular perturbation of linear differential equations

Chapter 3. Degenerate boundary value problems

Chapter 4. Asymptotic solutions of partial differential equations

Chapter 5. Asymptotic solutions of nonlinear differential equations

References

Part 2. Thirteen Papers

Perturbation methods in eddy current testing

Buckling of thin cylindrical shells and shells of negative Gaussian curvature

Thermoelastic deformations of mirrors

A mathematical model for hydroelastic problems with a fluid memory. Part I

A mathematical model for hydroelastic problems with a fluid memory. Part II

Lowfrequency vibrations of cylindrical shells. Part I: Shells with a slanted edge

Lowfrequency vibrations of cylindrical shells. Part II: Connected shells

Buckling of convex shells under nonaxisymmetric loading

Elastoplastic deformations of ribbed plates

Elastic wave propagation through elastic shells

Dynmamic stability and forced vibrations of a horizontal rotor with a cracked shaft

Edge effect under large axisymmetric deformations of shells of revolution

Turning points and caustics in linear problems of thin shell free vibrations and buckling