Structural stability and vibration : an integrated introduction by analytical and numerical methods /: an integrated introduction by analytical and numerical methods. ([2018])

• Record Type: Book
• Further Information: Note: Sine Leergaard Wiggers, Pauli Pedersen.
• Authors: Wiggers, Sine Leergaard; Pedersen, Pauli, 1937-
• 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. 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. 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. 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. 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource, illustrations
• Subjects: 515/.392; Engineering; Stability; Vibration -- Mathematical models; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Stability; Vibration -- Mathematical models; Engineering; Vibration, Dynamical Systems, Control; Numerical and Computational Physics, Simulation; Mechanical Statics and Structures; Science -- Mathematical Physics; Technology & Engineering -- Engineering (General); Mathematical physics; Mechanics of solids; Vibration; Statics; Technology & Engineering -- Mechanical; Dynamics & vibration; Electronic books
• Languages: English
• ISBNs: 9783319727219; 3319727214
• Related ISBNs: 9783319727202; 3319727206
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed February 21, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.