Dynamic Stability of Columns under Nonconservative Forces [electronic resource] : Theory and Experiment /
Sugiyama, Yoshihiko.author.
Langthjem, Mikael A.author.
Katayama, Kazuo.author.
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 deals with the divergence of Euler’s column under a dead (conservative) loading from a view point of dynamic stability. Three experiments with cantilevered columns under a rocket-based follower force are described to present the verifiability of nonconservative problems of structural stability. Dynamic stability of columns under pulsating forces is discussed through analog experiments, and by analytical and experimental procedures together with related theories. Throughout the volume the authors retain a good balance between theory and experiments on dynamic stability of columns under nonconservative loading, offering a new window to dynamic stability of structures, promoting student- and scientist-friendly experiments.
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’s Approach 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. .
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 deals with the divergence of Euler’s column under a dead (conservative) loading from a view point of dynamic stability. Three experiments with cantilevered columns under a rocket-based follower force are described to present the verifiability of nonconservative problems of structural stability. Dynamic stability of columns under pulsating forces is discussed through analog experiments, and by analytical and experimental procedures together with related theories. Throughout the volume the authors retain a good balance between theory and experiments on dynamic stability of columns under nonconservative loading, offering a new window to dynamic stability of structures, promoting student- and scientist-friendly experiments.
Mechanics.
Mechanics, Applied.
Engineering design.
Partial differential equations.
Mathematical physics.
Energy systems.
Solid Mechanics.
Engineering Design.
Partial Differential Equations.
Theoretical, Mathematical and Computational Physics.
Energy Systems.