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Dynamic Stability of Columns under Nonconservative Forces Theory and Experiment

This book treats dynamic stability of structures under nonconservative forces. It is not a mathematics-based, but rather a dynamics-phenomena-oriented monograph, written with a full experimental background. Starting with fundamentals on stability of columns under nonconservative forces, it then deal...

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Bibliographic Details
Main Authors: Sugiyama, Yoshihiko, Langthjem, Mikael A. (Author), Katayama, Kazuo (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2019, 2019
Edition:1st ed. 2019
Series:Solid Mechanics and Its Applications
Subjects:
Mechanical Power Engineering
Mechanics, Applied
Electric Power Production
Engineering Design
Solids
Electrical Power Engineering
Solid Mechanics
Mathematical Physics
Differential Equations
Theoretical, Mathematical And Computational Physics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 14.8 Discussion
  • References
  • 15 Parametric Resonances of Columns with Damping
  • 15.1 Approaches to Mathieu-Hill Equations
  • 15.2 Hsu’sApproach to Coupled Hill Equations
  • 15.3 Effect of Damping
  • 15.4 Second-order Approximation
  • 15.5 Discussion
  • References
  • 16 Columns under a Pulsating Reut Force
  • 16.1 Columns under a Pulsating Generalized Reut Force
  • 16.2 Finite Difference Formulation and Stability Analysis
  • 16.3 Experiment with Columns under a Pulsating Reut Force
  • 16.4 Discussion
  • References
  • 17 Remarks about Approaches to the Dynamic Stability of Structures
  • References
  • Appendix: Suggested Exercises.
  • 5.2 Equation of Motion and Stability Analysis
  • 5.3 Energy Expressions
  • 5.4 Flutter Configurations and Phase Angles Functions
  • 5.5 Energy Balance with Small Internal Damping
  • 5.6 Energy Balance with Both Internal and External Damping
  • 5.7 Energy Growth Rate
  • 5.8 Introduction of Small Internal Damping at the Undamped Flutter Bound
  • 5.9 Discussion
  • References
  • 6 Cantilevered Pipes Conveying Fluid
  • 6.1 Basic Equations of Motion
  • 6.2 Finite Element Formulation
  • 6.3 Eigenvalue Branches Related to Flutter
  • 6.4 Flutter Configurations
  • 6.5 Effect of Internal Damping
  • 6.6 Discussion
  • References
  • 7 Cantilevered Pipes with a Mechanical Element
  • 7.1 Pipes with an Elastic Spring
  • 7.2 Pipes with a Lumped Mass
  • 7.3 Pipes with a Damper
  • 7.4 Coefficient of Damping of a Dashpot Damper
  • 7.5 Discussion
  • References
  • 8 Columns under a Follower Force with a Constant Line of Action
  • 8.1 Reut’s Column
  • 8.2 Stability Analysis of a Generalized Reut’s Column
  • 8.3 Approximate Solution by the Galerkin Method
  • 8.4 Non-self-adjointness of Boundary Value Problems
  • 8.5 Discussion
  • References
  • 9 Generalized Reut’s Column
  • 9.1 Stability Analysis
  • 9.2 Realization of Reut Force
  • 9.3 Experimental Setup
  • 9.4 Experimental Results
  • 9.5 Reut’s Column with a Damper
  • 9.6 Discussion
  • References
  • 10 Columns under a Rocket-based Follower Force
  • 10.1 Equation of Motion and Stability Analysis
  • 10.2 Rocket Motors
  • 10.3 Test Columns
  • 10.4 Preliminary Tests
  • 10.5 Flutter Test
  • 10.6 Discussion
  • References
  • 11 Columns under a Rocket-based Follower Force and with a Lumped Mass
  • 11.1 Finite Element Formulation and Stability Analysis
  • 11.2 Rocket Motors
  • 11.3 Estimate of the Effect of a Lumped Mass on the Flutter Limit
  • 11.4 Flutter Test
  • 11.5 Discussion
  • References
  • 12 Columns under a Rocket-based Subtangential Follower Force
  • Preface
  • 1 Fundamentals
  • 1.1 Beam and Column
  • 1.2 Stability and Stability Criteria
  • 1.3 Experiments with Columns
  • 1.4 Preliminary Tests
  • 1.5 Influence of Support Conditions
  • 1.6 Nonconservative Forces
  • 1.7 Discussion
  • References
  • 2 Columns under Conservative Forces
  • 2.1 Cantilevered Columns
  • 2.2 Pinned-pinned Columns
  • 2.3 Standing Cantilevered Columns
  • 2.4 Discussion
  • References
  • 3 Columns under a Follower Force
  • 3.1 Beck’s Column
  • 3.2 Vibrations of Beck’s Column
  • 3.3 Stability in a Finite Time Interval
  • 3.4 Character of Beck’s Column
  • 3.5 Nonconservative Nature of a Follower Force
  • 3.6 Discussion
  • References
  • 4 Columns with Damping
  • 4.1 Cantilevered Columns with Damping
  • 4.2 Stability Analysis
  • 4.3 Beck’s Column with Damping Introduced
  • 4.4 Pflüger’s Column with Internal Damping
  • 4.5 Dynamic Responses
  • 4.6 Discussion
  • References
  • 5 Energy Consideration on the Role of Damping
  • 5.1 Energy Considerations
  • 12.1 Mathematical Model and Finite Element Formulation
  • 12.2 Rocket Motors
  • 12.3 Test Columns
  • 12.4 Stability Estimates
  • 12.5 Experiment with Columns under a Rocket-based Subtangential Follower Force
  • 12.6 Discussion
  • References
  • 13 Pinned-pinned Columns under a Pulsating Axial Force
  • 13.1 The Mathieu Equation
  • 13.2 Stability of the Solution to the Mathieu Equation
  • 13.3 Pinned-pinned Columns
  • 13.4 Vibrations in the Vicinity of Upper and Lower Boundaries I
  • 13.5 Vibrations in the Vicinity of Upper and Lower Boundaries II
  • 13.6 Effect of a Phase Angle in Excitation
  • 13.7 Discussions
  • References
  • 14 Parametric Resonances of Columns
  • 14.1 Mathieu-Hill Equations
  • 14.2 Hsu’s Approach
  • 14.3 Coupled Mathieu Equation of Columns
  • 14.4 Hsu’s Resonance Conditions
  • 14.5 Estimate of the Principal Regions of Resonances
  • 14.6 Experiment with Columns Having Clamped-clamped and Clamped-pinned Ends
  • 14.7 Columns under a Pulsating Follower Force

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