Stability and bifurcation of structures : statical and dynamical systems / Angelo Luongo, Manuel Ferretti, Simona Di Nino.
Luongo, Angelo, author.; Ferretti, Manuel, author.; Di Nino, Simona, author.
2023
TA351 .L86 2023
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Title Stability and bifurcation of structures : statical and dynamical systems / Angelo Luongo, Manuel Ferretti, Simona Di Nino.
Author Luongo, Angelo, author.
ISBN 9783031275722 electronic book
3031275721 electronic book
3031275713
9783031275715
DOI https://doi.org/10.1007/978-3-031-27572-2
Published Cham : Springer, 2023.
Language English
Description 1 online resource (712 p.)
Item Number 10.1007/978-3-031-27572-2 doi
Call Number TA351 .L86 2023
Dewey Decimal Classification 624.171
Summary This book overcomes the separation existing in literature between the static and the dynamic bifurcation worlds. It brings together buckling and post-buckling problems with nonlinear dynamics, the bridge being represented by the perturbation method, i.e., a mathematical tool that allows for solving static and dynamic problems virtually in the same way. The book is organized as follows: Chapter one gives an overview; Chapter two illustrates phenomenological aspect of static and dynamic bifurcations; Chapter three deals with linear stability analysis of dynamical systems; Chapter four and five discuss the general theory and present examples of buckling and post-buckling of elastic structures; Chapter six describes a linearized approach to buckling, usually adopted in the technical literature, in which pre-critical deformations are neglected; Chapters seven to ten, analyze elastic and elasto-plastic buckling of planar systems of beams, thin-walled beams and plate assemblies, respectively; Chapters eleven to thirteen, illustrate dynamic instability phenomena, such as flutter induced by follower forces, aeroelastic bifurcations caused by wind flow, and parametric excitation triggered by pulsating loads. Finally, Chapter fourteen discusses a large gallery of solved problems, concerning topics covered in the book. An Appendix presents the Vlasov theory of open thin-walled beams. The book is devoted to advanced undergraduate and graduate students, as well as engineers and practitioners. The methods illustrated here are immediately applicable to model real problems. The Book Introduces, in a simple way, complex concepts of bifurcation theory, by making use of elementary mathematics Gives a comprehensive overview of bifurcation of linear and nonlinear structures, in static and dynamic fields Contains a chapter in which many problems are solved, either analytically or numerically, and results commented.
Note Equilibrium Equation for Imperfect System
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based upon online resource; title from PDF title page (viewed July 3rd, 2023).
Added Author Ferretti, Manuel, author.
Di Nino, Simona, author.
Available in Other Form Stability and Bifurcation of Structures
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Record Appears in Online Resources > Ebooks
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Intro
Preface
Contents
1 Introduction
1.1 Basic Concepts
1.2 Overview of the Book
1.3 Book Style
2 Phenomenological Aspects of Bifurcation of Structures
2.1 Introduction
2.2 Stability and Bifurcation
2.2.1 Equilibrium Points
2.2.2 Stability of Equilibrium
Lagrange-Dirichlet Theorem
2.2.3 Bifurcation
Bifurcation of Equilibrium
Static and Dynamic Bifurcations
2.3 An Example of Static Bifurcation: The Euler Beam
2.4 Static Bifurcations of Elastic Structures
2.4.1 Fork and Transcritical Bifurcations
2.4.2 Snap-Through Phenomenon

2.4.3 Interaction Between Simultaneous Modes
An Example of a Two-Parameter Family: The Compressed Truss
Structural Optimization in the Linear Optics
Nonlinear Interaction Between Simultaneous Modes
2.5 Dynamic Bifurcations of Elastic Structures Subject to Nonconservative Forces
2.5.1 Flutter Induced by Follower Forces
2.5.2 Galloping Induced by Aerodynamic Flow
2.5.3 Parametric Excitation Induced by Pulsating Loads
References
3 Stability and Bifurcation Linear Analysis
3.1 Introduction
3.2 Dynamical Systems
3.3 Mechanical Systems

3.4 Linear Stability Analysis
3.4.1 Conservative Systems
3.4.2 Circulatory Systems
3.4.3 Influence of Damping
Damped Conservative Systems
Damped Circulatory Systems
3.5 An Illustrative Example: The Planar Mathematical Pendulum
3.5.1 Equation of Motion and the Phase Portrait
Equilibrium Points
Phase Portrait
3.5.2 Local Stability Analysis
Center Point (Lower Equilibrium Position)
Saddle Point (Upper Equilibrium Position)
3.5.3 Energy Criterion of Stability
3.5.4 Effect of Damping
Equation of Motion
Local Stability Analysis

3.6 Bifurcations of Autonomous Systems
3.6.1 Equilibrium Paths
3.6.2 Bifurcations from a Trivial Path
3.6.3 Bifurcations from a Non-trivial Path
Linearized Equation of Motion
Bifurcation Analysis
3.6.4 Bifurcation Mechanisms for Conservative and Circulatory Systems, without or with Damping
Conservative Systems
Circulatory Systems
Damped Conservative Systems
Damped Circulatory Systems
References
4 Buckling and Postbuckling of Conservative Systems
4.1 Introduction
4.2 Static Analysis of Conservative Systems
4.3 Classification of the Equilibrium Points

4.4 Numerical Continuation Methods
4.4.1 Newton-Raphson Method
4.4.2 Sequential Continuation
Sequential Continuation Failure
4.4.3 Arclength Method
4.5 Asymptotic Analysis of Bifurcation from Trivial Path
4.5.1 Linear Stability Analysis
Adjacent Equilibrium Criterion
4.5.2 Nonlinear Bifurcation Analysis
Asymptotic Expression of the Bifurcated Path
Normalization
Perturbation Equations
Solution to the Perturbation Equations
Case of Symmetric Systems
4.6 Effect of Imperfections
4.6.1 Equilibrium Equations
Geometric Imperfections
Load Imperfections

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