Dynamic instability of parabolic shells in supersonic gas stream

Аврамов, К. В.; Chernobryvko, Marina; Kazachenko, O.; Batutina, T. J.

doi:10.1007/s11012-015-0247-4

Cited by 13 publications

(7 citation statements)

References 35 publications

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“…Надзвуковий потік, який рухається паралельно осі симетрії конструкції, описується поршне-Н. Г. Сахно, К. В. Аврамов, Б. В. Успенський вою теорією [3,12,17]:…”

Section: динамічна система зі скінченною кількістю ступенів свободиunclassified

Dynamic instability of a compound nanocomposite shell

Sakhno¹,

Аврамов²,

Uspensky³

2021

Kosm. nauka tehnol.

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Free oscillations and dynamic instability due to supersonic airflow pressure are investigated in a functional-gradient compound composite conical-cylindrical shell made of a carbon nanotubes-reinforced material. Nanocomposite materials with a linear distribution of the volumetric fraction of nanotubes over the thickness are considered. Extended mixture rule is used to estimate nanocomposite’s mechanical characteristics. A high-order shear deformation theory is used to represent the shell deformation. The assumed-mode technique, along with a Rayleigh-Ritz method, is applied to obtain the equations of the structure motion. To analyze the compound structure dynamics, a new system of piecewise basic functions is suggested. The pressure of a supersonic flow on the shell is obtained by using the piston theory. An example of the dynamic analysis of a nanocomposite conical-cylindrical shell in the supersonic gas flow is considered. The results of its modal analysis using the Rayleigh-Ritz technique are close to the natural frequencies of the shell obtained by finite element analysis. In this case, finite element analysis can only be used for shells made of material with a uniform distribution of nanotubes over the thickness. The dependence of the natural frequencies of a compound shell on the ratio of the lengths of the conical and cylindrical parts is studied. The dependence of the critical pressure of a supersonic flow on the Mach numbers and the type of carbon nanotubes reinforcement is investigated. Shells with a concentration of nanotubes predominantly near the outer and inner surfaces are characterized by higher values of natural frequencies and critical pressure than the shells with a uniform distribution of nanotubes or with a predominant concentration of nanotubes inside the shell.

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Section: динамічна система зі скінченною кількістю ступенів свободиunclassified

Dynamic instability of a compound nanocomposite shell

Sakhno¹,

Аврамов²,

Uspensky³

2021

Kosm. nauka tehnol.

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“…The development of ways and means of creating reliable power shell structures in industrial, civil, chemical and aerospace engineering, and in other areas includes a significant range of theoretical, experimental, technological and computer-software problems. The creation of adequate mathematical models and methods of calculating the local and overall stability under combined loading, the study of new mechanical effects and phenomena that can significantly increase the bearing capacity of the developed structures and systems with a reduction in their material consumption should be related to these problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Improving the shell structure stability is achieved, in particular, by using the reinforcing elements in the form of longitudinal and transverse structural frames.…”

Section: Introductionmentioning

confidence: 99%

“…Under the prevailing action of an external pressure on a thin shell of rotation, the transverse reinforcement with intermediate rings is the most effective, and the discreteness consideration of their location allows us to offer rational stiffness characteristics of the structures being researched on the basis of studying the local and overall forms of buckling [1][2][3][4][5], and changes in the geometric shape of the middle surface [6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Axial force effect on the overall buckling of a compound reinforced shell structure with the positive Gaussian curvature at an external pressure

Gristchak¹,

Dyachenko²

2020

Mathematical and Computer Modelling of Engineering Systems

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“…Zhang investigated the stability and bifurcation behaviors of a two-dimensional, nonlinear, viscoelastic panel in supersonic flow, using analytical and numerical methods [15]. Avramov et al analyzed the dynamic instability of the parabolic shells in a supersonic gas flow numerically [16]. Chen et al studied the coefficients of the characteristic equation of the first approximation system and its corresponding Hurwitz determinant, which is used to derive the algebraic criterion of Hopf bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation of Heated Panels Flutter in Supersonic Flow

Cao

Yao

2019

Mathematics

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A differential equation of panel vibration in supersonic flow is established on the basis of the thin-plate large deflection theory under the assumption of a quasi-steady temperature field. The equation is dimensionless, and the derivation of its second-order Galerkin discretization yields a four-dimensional system. The algebraic criterion of the Hopf bifurcation is applied to study the motion stability of heated panels in supersonic flow. We provide a supplementary explanation for the proof process of a theorem, and analytical expressions of flutter dynamic pressure and panel vibration frequencies are derived. The conclusion is that the algebraic criterion of Hopf bifurcation can be applied in high-dimensional problems with many parameters. Moreover, the computational intensity of the method established in this work is less than that of conventional eigenvalue computation methods using parameter variation.

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Dynamic instability of parabolic shells in supersonic gas stream

Cited by 13 publications

References 35 publications

Dynamic instability of a compound nanocomposite shell

Dynamic instability of a compound nanocomposite shell

Axial force effect on the overall buckling of a compound reinforced shell structure with the positive Gaussian curvature at an external pressure

Hopf Bifurcation of Heated Panels Flutter in Supersonic Flow

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