CHAOTIC VIBRATIONS OF CLOSED CYLINDRICAL SHELLS IN A TEMPERATURE FIELD

2008 ◽  
Vol 18 (05) ◽  
pp. 1515-1529 ◽  
Author(s):  
A. V. KRYSKO ◽  
J. AWREJCEWICZ ◽  
E. S. KUZNETSOVA ◽  
V. A. KRYSKO
Keyword(s):  
Cylindrical Shell ◽  
Temperature Field ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Novel ◽  
Fourier Methods ◽  
Constant Stiffness ◽  
Chaotic Vibrations ◽  
Qualitative Changes ◽  
Shell Dynamics

A closed cylindrical shell with circular cross-section having constant stiffness and density and subjected to sign changeable loading and embedded into a temperature field is analyzed. Both Bubnov–Galerkin (with a higher approximation) and Fourier methods are applied to solve the derived nonlinear nondimensional partial differential equations. Among others, the novel scenario of transition from shell harmonic to chaotic vibrations via the collapse of quasi-periodic vibrations with one independent frequency and Hopf bifurcation is detected, illustrated and discussed. In addition, it is shown how for various intensities of the temperature field (including its absence) the increase of the loading yields qualitative changes in the investigated shell dynamics, and how chaotic zones are transmitted into periodic ones and vice versa.

Buckling of Semimonocoque Structures Under Compression

1942 ◽  
Vol 9 (3) ◽  
pp. A117-A121
Author(s):  
Tsun Kuei Wang
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Cross Section ◽  
Compressive Load ◽  
Circular Cross Section ◽  
Critical Value ◽  
Cylindrical Structure ◽  
Stiffened Cylindrical Shell ◽  
Thin Tube ◽  
Longitudinal Stiffeners

Abstract This paper presents an investigation of the strength of a stiffened cylindrical shell under the action of uniform axial compression. It is assumed that the cylindrical structure is a very thin tube of circular cross section; its reinforcements consist essentially of a great number of uniform longitudinal stiffeners and a great number of uniform transverse rings. It is often desirable to know the critical value of the compressive load for the buckling of such a structure.

scholarly journals Chaotic Vibrations of Closed Cylindrical Shells in a Temperature Field

2008 ◽  
Vol 15 (3-4) ◽  
pp. 335-343 ◽  
Author(s):  
A.V. Krysko ◽  
J. Awrejcewicz ◽  
E.S. Kuznetsova ◽  
V.A. Krysko
Keyword(s):  
Temperature Field ◽  
Galerkin Method ◽  
Cylindrical Shells ◽  
Influence Of Temperature ◽  
Fourier Representation ◽  
Chaotic Vibrations ◽  
Shell Dynamics

Complex vibrations of cylindrical shells embedded in a temperature field are studied, and the Bubnov-Galerkin method in higher approximations and in the Fourier representation is applied. Both lack and influence of temperature field on the shell dynamics are analyzed.

scholarly journals Refinement of the Maxwell formula for a composite reinforced by circular cross-section fibres. Part II: using Padé approximants

2020 ◽  
Vol 231 (12) ◽  
pp. 5145-5157
Author(s):  
Igor I. Andrianov ◽  
Jan Awrejcewicz ◽  
Galina A. Starushenko ◽  
Vladimir A. Gabrinets
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Volume Fraction ◽  
Effective Properties ◽  
Circular Cross Section ◽  
The Novel ◽  
High Contrast ◽  
Asymptotic Results ◽  
Reinforced Composite ◽  
Coefficient Of Thermal Conductivity

Abstract The effective properties of the fiber-reinforced composite materials with fibers of circle cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For an analytical solution of the periodically repeated cell problem the Schwarz alternating process (SAP) was employed. Convergence of this method was proved by S. Mikhlin, S. Sobolev, V. Mityushev. Unfortunately, the rate of the convergence is often slow, especially for nondilute high-contrast composite materials. For improving this drawback we used Padé approximations for various forms of SAP solutions with the following additive matching of obtained expressions. As a result, the solutions in our paper are obtained in a fairly simple and convenient form. They can be used even for a volume fraction of inclusion very near the physically possible maximum value as well as for high-contrast composite constituents. The results are confirmed by comparison with known numerical and asymptotic results.

Routes to Chaos Exhibited by Closed Flexible Cylindrical Shells

2006 ◽  
Vol 2 (1) ◽  
pp. 1-9 ◽  
Author(s):  
J. Awrejcewicz ◽  
V. Krysko ◽  
N. Saveleva
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Cross Section ◽  
Cylindrical Shells ◽  
Circular Cross Section ◽  
Qualitative Theory ◽  
The Other ◽  
Chaotic Vibrations ◽  
Runge Kutta Method ◽  
The Cauchy Problem

Complex vibrations of closed cylindrical shells of circular cross section and finite length subjected to nonuniform sign-changeable external load in the frame of classical nonlinear theory are studied. A transition from partial differential equations to ordinary differential equations (Cauchy problem) is carried out using the higher order Bubnov–Galerkin’s approach and Fourier’s representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. Results are analyzed owing to the application of nonlinear dynamics and qualitative theory of differential equations. The present work is devoted to the analysis of influence of the system dynamics of the following parameters: length of pressure width φ0, relative linear shell dimension λ=L∕R, and frequency ωp and amplitude q0 of external transversal load. Some new scenarios of vibrations of closed cylindrical shells exhibiting a transition from harmonic to chaotic vibrations are illustrated and studied.

scholarly journals Refinement of the Maxwell formula for composite reinforced by circular cross-section fibers. Part I: using the Schwarz alternating method

2020 ◽  
Vol 231 (12) ◽  
pp. 4971-4990 ◽  
Author(s):  
Igor I. Andrianov ◽  
Jan Awrejcewicz ◽  
Galina A. Starushenko ◽  
Vladimir A. Gabrinets
Keyword(s):  
Cross Section ◽  
Effective Properties ◽  
Circular Cross Section ◽  
Principal Term ◽  
The Novel ◽  
Asymptotic Results ◽  
Asymptotic Homogenization ◽  
Schwarz Alternating Method ◽  
Reinforced Composite ◽  
Coefficient Of Thermal Conductivity

Abstract The effective properties of the fiber-reinforced composite materials with fibers of circular cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For analytical solution of the periodically repeated cell problem, the Schwarz alternating process is employed. The principal term of the refined formula coincides with the classical Maxwell formula. On the other hand, the refined formula can be used far beyond the area of applicability of the Maxwell formula. It can be used for dilute and non-dilute composites. It is confirmed by comparison with known numerical and asymptotic results.

scholarly journals Stability Of A Cylindrical Shell

2021 ◽  
Vol 03 (04) ◽  
pp. 166-171
Author(s):  
Shakhrukh Muratovich Davlyatov ◽  
◽  
Khusnitdin Akhrarovich Akramov ◽  
Keyword(s):  
Cylindrical Shell ◽  
Cross Section ◽  
Circular Cross Section ◽  
Loss Of Stability

Results of researches of stability of the cylindrical cover of circular cross section consisting of several layers at a zagruzheniye the external evenly distributed loading are given in this article. Settlement dependences are offered, critical loadings, opkredelena of a form of loss of stability of a cover are found.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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