| Description |
1 online resource (xvi, 158 pages : illustrations |
| Series |
Springer tracts in mechanical engineering |
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Springer tracts in mechanical engineering.
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| Contents |
Intro; Preface; Contents; Acronyms; Notations; 1 Introduction; 2 Beam-Column Differential Equation; 2.1 What Is a Beam-Column; 2.2 Differential Equation for Static Equilibrium; 2.3 Differential Equation for Eigenfrequencies; 2.4 Names and Symbols for Boundary Conditions (BC); 3 Eigen Solutions for the Euler Cases; 3.1 Boundary Conditions; 3.2 How to Solve an Eigenvalue Problem; 3.3 Instability Modes for the Euler Cases; 3.3.1 Instability Mode for the Euler Case I; 3.3.2 Instability Modes for the Euler Cases IIâ#x80;#x93;IV; 3.3.3 Instability Mode for the Euler Case V |
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3.4 Eigenfrequency Modes for the Euler Cases3.4.1 Eigenfrequency Modes for the Euler Case I; 3.4.2 Eigenfrequency Modes for the Euler Cases IIâ#x80;#x93;VI; 3.5 Summary; 4 Beam-Columns and Applied Berry Functions; 4.1 Model of Beam-Column; 4.2 General Moment Loads; 4.3 Elastic Support Against End Rotations; 4.3.1 A Fixed Support as a Limiting Case; 5 Shear Beam Loads and Cantilever Beam-Columns; 5.1 Shear Loads on Beam-Columns; 5.1.1 A Fixed Support as a Limiting Case; 5.2 Cantilever Beam-Columns; 5.2.1 Two Cantilever Cases; 6 Beam-Column Eigenfrequencies |
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6.1 Mathmatical Model for Different Physical Problems6.2 Solution of DE (6.1) with BC (6.2); 6.3 Eigenfrequency as a Function of Conservative Axial Load; 6.4 Rotational Spring Supports; 6.4.1 Euler Cases as Limiting Cases; 7 Buckling with Spring Supported BC; 7.1 Mathematical Definition and Physical Experiments; 7.2 Different Instability Formulations; 7.3 Buckling with End Rotations; 7.4 Buckling with End Translations; 7.5 Buckling with Winkler Support; 7.5.1 Eigenfrequencies with Winkler Support; 8 Eigenfrequencies of Beam-Columns with Spring Supported BC |
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8.1 Eigenvalue Problems with Analytical Solution8.2 Solving the Transcendental Equations; 8.3 Explicit Solutions by Inverse Approach; 8.3.1 Lowest Eigenfrequency as a Function of Support Stiffnesses, Assumed No Column Force; 8.4 Alternative Function Expressions; 8.5 Specific Graphically Presented Results, Obtained by the Newtonâ#x80;#x93;Raphson Method; 8.5.1 Lowest Eigenfrequency as a Function of Column Force, with Support Stiffnesses as Parameters; 8.5.2 Lowest Eigenfrequency as a Function of Column Force, Further BC Parameters |
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8.6 Lowest Eigenfrequency as a Function of Non-conservative ̀̀follower'' Column Force9 Dynamic Stability Formulation; 9.1 One and Two Degrees of Freedom; 9.2 An Elementary Beam-Column Case; 9.3 Column with a Point Mass; 9.4 An Improved Dynamic Column Model; 9.5 Non-conservative Column Load; 10 Stability of 2D Frames; 10.1 Frames; 10.2 Only One Beam-Column in the Frame; 10.3 Several Beam-Columns in the Frame; 10.4 Solution Procedure (̀̀cookbook''); 10.5 Post-Critical Imperfection Analysis; 11 Buckling Stresses, Material Nonlinearity, and Beam Modeling; 11.1 Various Concepts |
| Summary |
This book offers an integrated introduction to the topic of stability and vibration. Strikingly, it describes stability as a function of boundary conditions and eigenfrequency as a function of both boundary conditions and column force. Based on a post graduate course held by the author at the University of Southern Denmark, it reports on fundamental formulas and makes uses of graphical representation to promote understanding. Thanks to the emphasis put on analytical methods and numerical results, the book is meant to make students and engineers familiar with all fundamental equations and their derivation, thus stimulating them to write interactive and dynamic programs to analyze instability and vibrational modes |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed February 21, 2018) |
| Subject |
Structural stability.
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Vibration -- Mathematical models
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structural stability.
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Mathematical physics.
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Mechanics of solids.
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Dynamics & vibration.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Stability
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Vibration -- Mathematical models
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| Form |
Electronic book
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| Author |
Pedersen, Pauli, 1937- author.
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| ISBN |
9783319727219 |
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3319727214 |
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