scholarly journals Numerical calculation of the natural vibration frequencies of thermo-elastic rods taking into account the effect of the temperature gradient

2021 ◽  
Vol 1901 (1) ◽  
pp. 012116
Author(s):  
O G Kikvidze ◽  
G G Sakhvadzeand ◽  
G Zh Sakhvadze
Keyword(s):  
Numerical Calculation ◽  
Temperature Gradient ◽  
Natural Vibration ◽  
Elastic Rods ◽  
Vibration Frequencies

NUMERICAL CALCULATION OF THE NATURAL VIBRATION FREQUENCIES OF THERMO-ELASTIC RODS TAKING INTO ACCOUNT THE EFFECT OF THE TEMPERATURE GRADIENT

2021 ◽  
Author(s):  
O. G. Kikvidze ◽  
◽  
G. G. Sakhvadze ◽  
G. Zh. Sakhvadze ◽  
◽  
...  
Keyword(s):  
Numerical Calculation ◽  
Temperature Gradient ◽  
Natural Vibration ◽  
Elastic Rods ◽  
Vibration Frequencies

Рассматриваются упругие стержневые элементы, осевая линия которых в естественном состоянии есть плоская кривая, и после нагружения остается плоской кривой. Используются следующие допущения: поперечные нормальные сечения, плоские до деформации, остаются плоскими и нормальными к деформированной термоупругой осевой линии после деформации; температурное поле стационарное и неоднородное. Получены нелинейные уравнения движения стержня с учетом инерции вращения поперечного сечения и растяжимости осевой линии.

Simplified characteristics of active magnetic bearings

2002 ◽  
Vol 216 (5) ◽  
pp. 623-628 ◽  
Author(s):  
D J Peel ◽  
C M Bingham ◽  
Y Wu ◽  
D Howe
Keyword(s):  
Natural Vibration ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Viscous Damping ◽  
Vibration Frequencies ◽  
Active Magnetic Bearings ◽  
Complex Dynamic ◽  
Speed Range ◽  
Constant Coefficients ◽  
System Characteristics

Traditionally, active magnetic bearing (AMB) systems are designed as an integral component of machines having generally complex dynamic characteristics. An AMB supported rotor has been tested over a speed range that included system natural vibration frequencies. A linear stiffness and viscous damping AMB characteristic with constant coefficients was identified which was independent of the overall system characteristics and which can thus provide simple and transferable data for a machine designer.

Influence of Gravity and Taper on the Vibration of a Standing Column

2012 ◽  
Vol 4 (04) ◽  
pp. 483-495 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Cross Section ◽  
Numerical Stability ◽  
Natural Vibration ◽  
Vibration Frequencies ◽  
Stability Criteria ◽  
Initial Value ◽  
Vertical Column ◽  
Stability Boundaries ◽  
Section Shape ◽  
The Stability

AbstractThe stability and natural vibration of a standing tapered vertical column under its own weight are studied. Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column. For vibrations we use an accurate, efficient initial value numerical method for the first three frequencies. Four kinds of columns with linear taper are considered. Both the taper and the cross section shape of the column have large influences on the vibration frequencies. It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency. Vibrations may occur in two different planes.

scholarly journals Finite elements apparatus in thin-walled rods dynamics problems

2018 ◽  
Vol 245 ◽  
pp. 08007 ◽  
Author(s):  
Vladimir Rybakov ◽  
Stanislav Dyakov ◽  
Daniil Sovetnikov ◽  
Artur Azarov ◽  
Sergey Ivanov
Keyword(s):  
Natural Vibration ◽  
Steel Structures ◽  
Vibration Frequencies ◽  
Construction Engineering ◽  
Shear Theory ◽  
Mass Matrices ◽  
Element System ◽  
Mathematical Problems ◽  
Thin Walled ◽  
Dynamics Problems

The calculation of thin-walled rods is extremely relevant problem of structural mechanics and not only from the scientific standpoint, but also due to the widespread use of so-called lightweight thin-walled steel structures for construction engineering sector. Regardless of a sufficiently large number of studies connected with the statics of thin-walled rods, the dynamics of such systems have not been thoroughly studied yet. Based on one of the forward-looking theories of calculation i.e. the semi-shear theory by Slicker, the paper provides a technique for solving the dynamics problems of thin-walled rods. The stiffness and mass matrices of the finite element system are obtained for linear approximation of the form functions, and the natural vibration frequencies of the rods are calculated. The obtained solution is accomplished by the extrapolation method of estimating the accuracy of numerical methods for solving mathematical problems.

scholarly journals Natural Vibrations of Repetitive Structures

2000 ◽  
Vol 16 (2) ◽  
pp. 85-95 ◽  
Author(s):  
Dajun Wang ◽  
C.-C. Wang
Keyword(s):  
Eigenvalue Problem ◽  
Natural Vibration ◽  
Eigenvalue Problems ◽  
Vibration Frequencies ◽  
Natural Vibrations

ABSTRACTNatural vibration frequencies and modes of repetitive structures, including symmetric, periodic, linking structures, are considered in this work. By using the repetition of the identical parts, we reduce the eigenvalue problem of the structure to a set of eigenvalue problems of lower dimensions associated with the parts. Special forms and properties of the modes of natural vibrations are observed.

scholarly journals The effect of an enclosed air cavity on a rectangular drum

1983 ◽  
Vol 24 (3) ◽  
pp. 343-349 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Green’S Function ◽  
Frequency Shift ◽  
Green's Function ◽  
Natural Vibration ◽  
Frequency Equation ◽  
Vibration Frequencies ◽  
Air Cavity ◽  
First Order ◽  
Degenerate Mode ◽  
Function Formulation

AbstractThe effect of an enclosed air cavity on the natural vibration frequencies of a rectangular membrane is investigated. The modes specified by an even integer are not affected. For the odd-odd modes, the frequency equation is found via a Green's function formulation and is solved to first order in a parameter representing the effect of the cavity of the rectangular drum. The frequencies are raised, with the fundamental being most affected. In the case of degeneracies, each degenerate mode contributes to the frequency shift, but the degeneracy itself is not broken to first order.

Similarity Relations for Vibrating Cylinder with Temperature Gradient across the Thickness

1965 ◽  
Vol 69 (654) ◽  
pp. 412-414 ◽  
Author(s):  
V. J. Modi
Keyword(s):  
Temperature Gradient ◽  
Dynamic Analysis ◽  
High Speed ◽  
Considerable Importance ◽  
Mode Shapes ◽  
Flight Vehicle ◽  
Vibration Frequencies ◽  
Structural Stiffness ◽  
Similarity Relations ◽  
Similarity Law

The dynamic analysis of heated structures is of considerable importance. Significant heating of a flight vehicle may take place at high speed causing reduction in its structural stiffness and vibration frequencies. Such changes in frequencies and mode shapes can substantially affect various static and dynamic aeroelastic instabilities.In general, availability of a similarity law simplifies the solution of a problem. The following presentation studies similarity relations existing between an unheated vibrating cylinder and one with temperature gradient across its thickness.

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