The fundamental structural mechanics of elastic systems: Oscillations and flutter

Autor: ,
Año: 2006
Idioma: English
Encuadernación: Rústica


Resumen del libro
A.P.Leschenko has offered a completely new approach to structural mechanics, which allowed for a unique technique for structural engineering to be developed. This new method is based on the following three discoveries made by the author:

— Phenomenon of separating torsional strains of elastic bars;

— Specific law of analogy in stability and oscillation of elastic systems;

— Principle of force factors pairing in structural mechanics.

All actual approaches and theories of structural mechanics widely employ such an abstract concept as generalized force, neglecting, however, a definite and practical concept of external force factor. In author’s opinion, this breaks the interrelations between the external and internal forces acting on structures and the strains occurring in the structures, which leads to an implicit violation of the classical mechanics laws, namely the law of energy conservation, the Lagrange principle, and Newton’s laws. It should be stressed that Leschenko does not suggest that one concept should be simply replaced by the other, but interrelates the external action with other forces and factors concurrently acting on the structure.

Thus, the author has proposed to consider any elastic system as based on three permanently acting factors: 1) external forces; 2) internal forces; and 3) elastic strains; and indicated the principles linking the effects of these factors. Leschenko has developed a graphical scheme (the so-called triad) for an analysis of elastic systems. The triad analysis of elastic systems has enabled to reveal great contradictions in the available structural calculations of plates, shells and bars. On the other hand, the new method has allowed for an adequate model of stress-and-strain state of constructions to be developed, which, for the first time ever, has made it possible to predict with a high accuracy the moment of structural failure.

As main advantages of the new method we can list comparatively quick calculations of all types of structures, the examination and verification of design solutions, and the detection of critical loads and weak points of constructions. All these result in a considerable saving of materials, which is accompanied by improving the safety of constructions.


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Introduction and a brief historical review
Conventional symbols used in the book
Chapter 1. Description of the author’s invention
1.1. Calculation method to control catastrophic destruction
1.2. Description of invention
1.2.1. Object — phenomenon
1.2.2. Introduction
1.2.3. Justification of invention
1.2.4. Formula of invention
1.3. Description of invention
1.3.1. Object — law
1.3.2. Introduction
1.3.3. Justification of invention
1.3.4. Formula of invention
1.4. Description of invention
1.4.1. Object — law
1.4.2. Introduction
1.4.3. Justification of invention
1.4.4. Formula of invention
Chapter 2. The analogy method in oscillations of thin-walled constructions (a general linear theory of oscillations)
2.1. On some properties of constructions. A load coefficient. Statement of the problem on thin-walled bar oscillations
2.2. Classification of loads and symbols in the theory of oscillations
2.3. Possible forms of free oscillations of a thin-walled bar
2.4. Solution of differential equations of a bar’s free oscillations
2.5. Criterions of dynamical balance, stability and instability in oscillations. A concept of analogy in a form of free oscillations
2.6. The theorem on analogy at elastic systems’ oscillations
2.7. A qualitative method of solution of some equations of bars’ free oscillations
2.8. The method of analogy in calculations on beam’s oscillations loaded in the middle of the span with concentrated load
2.9. The analogy method in calculations on the oscillation of the pillar loaded by the load of eccentric compression
2.10. Experimental basis of the analogy method in oscillations of thin-walled constructions
2.11. The analogy method in calculations on oscillations of the beam loaded with the load evenly distributed along the span length
2.12. The analogy method in calculations of the beam’s oscillations loaded by concentrated moments on supports
2.13. The analogy method in calculations on oscillations of thin-walled plates and gentle cylindrical shells
Chapter 3. Application of the analogy method in calculations on oscillations of construction elements of bridges and aircrafts
3.1. Introduction
3.2. Calculation of a frame/beam bridge’s span structure on oscillations
3.3. A calculation of a carrier-rocket body on oscillations
3.4. The calculations of aircraft construction elements on oscillations
Chapter 4. The flutter theory as a particular case of general linear theory of oscillations
4.1. Introduction and analysis of modern concepts of the flutter theory
4.2. On some properties of consructions
4.3. Derivation of flutter’s differential equations and their solutions
4.4. The flutter of the beam loaded by a concentrated load in the middle of a span
4.5. The flutter of the post loaded by the load of eccentric compression
4.6. Experimental basis of the flutter theory
4.7. The flutter of the beam loaded with the load evenly distributed along the span’s length
4.8. The flutter of the beam loaded by concentrated moments on supports
4.9. The flutter of thin plates and gentle cylindrical shells
Chapter 5. Aircrafts’ flutter
5.1. Calculation of a carrier-rocket’s body on flutter
5.2. Calculation on flutter of an aircraft’s construction elements
Introduction and a brief historical review
The theory of oscillation processes is the field of the science associated with mathematics, mechanics and general physics.

I.Newton, L.Eiler, LaGrange and other classics of mechanics laid the basement of a modern theory of mechanical oscillations.

Khristian Huigens, the well-known Holland scientist and the watchmaker (1629–1695) contributed greatly into the theory of oscillation. He created izochronic cycloidal pendulum and was the first to observe selfsynchronization of associated oscillating systems.

J.Y.Strett (Lord Raley, 1842–1919) a British scientist created a systematic teaching on oscillation forms about their attenuation in the XIX century. he investigated a problem on plates’ and sheaths’ vibration in details.

At the same time A.Poincarre (1854–1912) for the first time proposed an idea of a qualitative analysis of oscillating systems using depiction of motion at a phase plane and related this depiction to the facts of periodical and nonperiodical motions, stability and so on.

He merited also a mathematical analysis of complex linear oscillations which he conceived in the form of a great number of ordinary linear oscillations.

The soviet scientists L.I.Mandelshtam (1879–1944), N.D.Papaleksi (1880–1947), A.A.Andropov (1901–1952), N.M.Krylov (1879–1955), N.N.Bogolyubov, Yu. A.Mitroopolsky, A.N.Krylov, V.V.Bolotin, I.I.Blechman, Yu. I.Neimark, Ya. G.Panovko, G.F.Ganiyev and others contributed greatly in creation of modern methods of theoretical analysis of oscillating systems.

Two directions may be singled out in the present science on oscillations:

1. Development of theory, schematization of real objects, creation ofidealized models using the laws of mechanics and mathematical apparatus;

2. Application of instruments for measurement of the values characterizing actual motion of one or another object. Experimental grounding of the theory by vibrodiagnostical methods.

The author carried out his investigations by these two directions.

He passed from the development of the linear theory of stability that has been covered in the previous books to elaboration of the linear theory of oscillations built on an idea of analogy in a form of free oscillations of constructions.

Varying a load, specifying the concepts of dynamical stability and instability taking into account the load’s effect by introducing the coefficient of the load, the author offers new scientific results which agree well with the experiment.

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