Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben

1990 | Buch

Introduction and Fundamental Concepts Kapitel lesen Erstes Kapitel lesen

Dynamic Stability of Suddenly Loaded Structures

verfasst von: George J. Simitses

Verlag: Springer New York

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

Dynamic instability or dynamic buckling as applied to structures is a term that has been used to describe many classes of problems and many physical phenomena. It is not surprising, then, that the term finds several uses and interpretations among structural mechanicians. Problems of parametric resonance, follower-force, whirling of rotating shafts, fluid-solid interaction, general response of structures to dynamic loads, and several others are all classified under dynamic instability. Many analytical and experimental studies of such problems can be found in several books as either specialized topics or the main theme. Two such classes, parametric resonance and stability of nonconservative systems under static loads (follower-force problems), form the main theme of two books by V. V. Bolotin, which have been translated from Russian. Moreover, treatment of aero elastic instabilities can be found in several textbooks. Finally, analytical and experimental studies of structural elements and systems subjected to intense loads (of very short duration) are the focus of the recent monograph by Lindberg and Florence. The first chapter attempts to classify the various "dynamic instability" phenomena by taking into consideration the nature of the cause, the character of the response, and the history of the problem. Moreover, the various concepts and methodologies as developed and used by the various investigators for estimating critical conditions for suddenly loaded elastic systems are fully described. Chapter 2 demonstrates the concepts and criteria for dynamic stability through simple mechanical models with one and two degrees of freedom.

Inhaltsverzeichnis

Frontmatter

Concepts and Criteria

Frontmatter
1. Introduction and Fundamental Concepts
Abstract
Dynamic stability or instability of elastic structures has drawn considerable attention in the past 30 years. The beginning of the subject can be traced to the investigation of Koning and Taub [1], who considered the response of an imperfect (half-sine wave), simply supported column subjected to a sudden axial load of specified duration. Since then, many studies have been conducted by various investigators on structural systems that are either suddenly loaded or subjected to time-dependent loads (periodic or nonperiodic), and several attempts have been made to find common response features and to define critical conditions for these systems. As a result of this, the term dynamic stability encompasses many classes of problems and many different physical phenomena; in some instances the term is used for two distincly different responses for the same configuration subjected to the same dynamic loads. Therefore, it is not surprising that there exist several uses and interpretations of the term.
George J. Simitses
2. Simple Mechanical Models
Abstract
Two single-degree-of-freedom mechanical models and one two-degree-of-freedom model are employed in this chapter to demonstrate the concept of dynamic stability for the extreme cases of the ideal impulse and sudden constant load of infinite duration. These models are typical of imperfection-sensitive structural configurations. They are kept as simple as possible, so that the emphasis can easily be placed on the concepts rather than on complex mathematical theories. For each model, the static stability analysis, based on the total potential energy approach, is given in detail. In addition, the total energy-phase plane approach is used for one model. For the same model, the equations of motion approach is also used, for demonstration and comparison purposes. The main emphasis, though, is placed on the total potential energy approach.
George J. Simitses
3. Dynamic Stability Under Constant Load of Finite Duration
Abstract
Consider a system (model) at its natural (unloaded) position. At time t=0 a constant load P is suddenly applied to the system and it acts only for a finite duration, time t = T0 (Figure 3.1). After the release of the force P, the system moves because of the energy imparted, during the action of the load P. The concept of dynamic stability for this particular load case is similar to the concept used in the cases of the ideal impulse and of the constant load of infinite duration. Thus, for all three cases the concept of dynamic stability is based on the definition of buckled and unbuckled motion.
George J. Simitses
4. The Influence of Static Preloading
Abstract
So far, in discussing the behavior of suddenly loaded structures, it has been assumed that the system is free of loading and that a step load is suddently applied for a given time duration. The cases of finite duration T0, see Figure 3.1, as well as the extreme cases of ideal impulse (T0➙0) and constant load of infinite duration (T 0➙∞), have been presented in the previous chapters. Although one may find several systems that fall in the category of initially load-free structures, in the world of structural configurations it is easier and more realistic to deal with initially preloaded structures. This means that the structure is first loaded quasi-statically and then is subjected to a dynamic load. Consider, for example, a submarine resting at the bottom of the ocean, at a reasonable depth. Then the submarine is subjected to a sudden blast load. This additional loading is the dynamic load, which can be idealized as an ideal impulse or a sudden load of finite duration T0.
George J. Simitses

Structural Applications

Frontmatter
5. The Concept of Dynamic Stability
Abstract
The beginning of dynamic instability and/or dynamic buckling can be traced to the investigation of Koning and Taub [1], who analyzed a suddenly loaded (in the axial direction) imperfect, simply supported column. Several studies followed in the 1940s and 1950s on the problem of dynamic column buckling. These studies [2–7] concentrated on such effects as those of axial inertia, of short and long duration of the load, of low- and high-velocity excitation, of in-plane inertia, of rotatory inertia, and of transverse shear. Similar studies continued into the 1970s [8–18] and the 1980s [19–20]. Moreover, nondeterministic consideration was included by Elishakoff [21–22] and extensions to plate geometries were reported by others [23–27]. A detailed discussion of geometries of this type is presented in Chapter 10. For these geometries, which under static conditions experience smooth buckling (the analysis shows that there exists s bifurcation point and the postbucking branch corresponds to stable static equilibrium positions), there is no clear criterion of instability, although the criterion used for establishing critical conditions is very simple. When some characteristics deflection increases rapidly with time, we have a dynamically critical condition. In reality, the problem of suddenlyy loaded columns and plates is one of dynamic response rather than one that encounters escaping (bucked) motion of some types. Parametric resonance is a possible dynamic instability for these configurations (see[28]).
George J. Simitses
6. Two-Bar Simple Frames
Abstract
The simple two-bar frame is a structural configuration that may or may not be imperfection-sensitive under static loading. This depends on the loading and boundary conditions. If both supports are immovable, and if the loading is a distributed load, the response is one of stable equilibrium and there is no possibility of static instability, either through the existence of a bifurcation point or through a limit point. Similarly, for the same supports, if the load is a concentrated one with a positive eccentricity (see Figure 6.1), the response is one of stable equilibrium (see [1–3]). On the other hand, if the eccentricity is zero or negative [1], the system is subject to limit point instability. For this case, the two-bar frame is sensitive to initial geometric imperfections and when the load is suddenly applied, critical conditions can easily be established by employing any of the three approaches discussed in Chapter 1. Moreover, if the support of the horizontal bar is movable along a vertical plane (Figure 6.1, model B), then the frame is imperfection sensitive for all loads. First the static analysis is presented and then the energy approach is employed for the estimation of critical conditions under sudden application of the load.
George J. Simitses
7. The Shallow Arch
Abstract
The first investigation of dynamic snap-through of shallow arches is due to Hoff and Bruce [1]. They considered the problem of a pinned arch with a half-sine-wave initial shape and a half-sine wave distributed lateral load. They treated the two extreme cases of sudden loads: that of constant magnitude and infinite duration and the ideal impusle case. Following this first paper, several studies are reported in the literature, in the middle to late 1960s, dealing with the arch configuration. These studies include the works of Lock [2], Hsu and his associates [3–6], and the Ph.D. thesis of the current author [7]. A short period after this, the arch problem was reinvestigated by employing the Budiansky-Roth [8] criterion. Please refer to Chapter 1 for a discussion of concepts, criteria, and estimates of critical conditions under suddenly applied loads. An attempt was made by Fulton and Barton [9] to introduce a different criterion for dynamic stability. The interested reader is also referred to the work of Lo and Masur [10] and of Huang and Nachbar [11], who added the effect of initial geometric imperfections and viscoelastic behavior. More recently, stability boundaries (interaction curves) were discussed by Gregory and Plaut [12] and Donaldson and Plaut [13] for arches that are loaded by two independent sets of dynamic loads applied in varying proportions to each other. The effect of damping on the dynamic buckling of low arches was investigated by Johnson [14].
George J. Simitses
8. The Shallow Spherical Cap
Abstract
Shallow spherical configurations, such as domes with small height-on-to spam ratios, can be subjected to sudden loads of various spatial distributions. Because of this, the designer of such systems is interested in their response and in particular in the level of the load under which snap-through can take place. This,of course, is a primary considerationin the design of these configurations.
George J. Simitses
9. Thin Cylindrical Shells
Abstract
Thin cylindrical shells of various constructions have been extensively used as structures or primary components in complex structural configurations. These systems are subjected to destabilizing loads in service, and since these loads are often dynamic in nature, it is not surprising that a great deal of interest was generated in the dynamic stability of cylindrical shells. Most of the analyses make use of monocoque metallic construction, but in this chapter applications to stiffened metallic and laminated composite configurations will also be presented.
George J. Simitses
10. Other Structural Systems
Abstract
As explained in Chapter 1, it is possible to extend the concept of dynamic buckling to all structural systems regardless of their behavior under static application of the loads (see Figures 1.6–1.10). This extension is discussed in Section 1.3, and it is based on limiting the deflectional response of a structure (when loaded suddenly), which is in agreement with requiring boundedness of deflectional response. One should observe that in limiting the deflectional response, boundedness is automatically satisfied (in some cases enforced), while the reverse is not true.
George J. Simitses
Backmatter
Metadaten
Titel
Dynamic Stability of Suddenly Loaded Structures
verfasst von
George J. Simitses
Copyright-Jahr
1990
Verlag
Springer New York
Electronic ISBN
978-1-4612-3244-5
Print ISBN
978-1-4612-7932-7
DOI
https://doi.org/10.1007/978-1-4612-3244-5