Dynamic Stability of Columns under Nonconservative Forces

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.- 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.- 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.- 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.