scholarly journals MATHEMATICAL MODELLING OF PROBLEM ON NON-LINEAR FLUTTER OF VISCO-ELASTIC SHELLS

2014 ◽  
pp. 94-98
Author(s):  
Bakhtiyar Khudayarov
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Viscoelastic Property ◽  
Critical Speed ◽  
Galerkin Methods ◽  
Basic Direction ◽  
Viscoelastic Cylindrical Shell ◽  
Current Value

In this work is investigated the flutter of viscoelastic cylindrical shell streamlined by gas current. The basic direction of work is consisted in taking into account of viscoelastic material’s properties at supersonic speeds. The vibration equations relatively of deflection are described by Integra-differential equations in partial derivatives. By Bubnov-Galerkin methods reduced the problems to investigation of system of ordinary Integro-Differential Equations (IDE). The IDE are solved by numerical method, which based on using of quadrature formula. The algorithm of the numerical solution on the basis of the method was described. Critical speeds for cylindrical shell flutter are defined. The influence of the viscoelastic property of the material, geometrical and aerodynamically non-linearity to the current value of critical speed and amplitude-frequency characteristics of the cylindrical shells was analyzed.

Stability of High Speed Rotors With Internal Friction

1974 ◽  
Vol 96 (3) ◽  
pp. 960-968 ◽  
Author(s):  
J. M. Vance ◽  
J. Lee
Keyword(s):  
Internal Friction ◽  
Differential Equations ◽  
Numerical Solution ◽  
High Speed ◽  
Critical Speed ◽  
Rotating Machinery ◽  
Rigid Foundation ◽  
Flexible Rotor ◽  
Mathematical Methods ◽  
The Stability

The problem of nonsynchronous whirl induced by internal friction is shown to be important when rotating machinery is designed for operation at supercritical speeds. Mathematical methods are used to determine the stability speed threshold of nonsyncronous whirl instability for an unbalanced flexible rotor on a rigid foundation. This threshold of instability is shown to be the same as the threshold for balanced rotors established by previous investigations. The location of the external damping (foundation or rotor) is shown to be important in determining stability when the foundation is made very rigid. The effect of shaft stiffness orthotropy on nonsynchronous whirl induced by internal friction is also investigated. Results from the stability analyses are verified by numerical solution of the differential equations. It is concluded that rotors can be safely operated up to speeds about eighty percent above the significant critical speed if the external damping is larger than the internal friction, and that shaft stiffness orthotropy has an insignificant effect on friction-induced whirl.

Flutter Analysis of Viscoelastic Sandwich Plate in Supersonic Flow

2005 ◽  
Author(s):  
B. A. Khudayarov
Keyword(s):  
Supersonic Flow ◽  
Differential Equations ◽  
Numerical Method ◽  
Quadrature Formula ◽  
Sandwich Plate ◽  
Galerkin Methods ◽  
Basic Direction ◽  
Partial Derivatives ◽  
Plate Flutter ◽  
Flutter Analysis

In this work is investigated the flutter of viscoelastic sandwich plate streamlined by gas current. The basic direction of work is consisted in taking into account of viscous-elastic material’s properties at supersonic speeds. The vibration equations relatively of deflection are described by Integro-Differential Equations (IDE) in partial derivatives. By Bubnov-Galerkin methods reduced the problems to investigation of system of ordinary IDE. The IDE are solved by numerical method, which based on using of quadrature formula. Critical speeds for sandwich plate flutter are defined.

scholarly journals MATHEMATICAL MODELLING OF THE ANALYTICAL AND NUMERICAL SOLUTION OF NON-STATIONARY INITIAL-VALUE PROBLEMS BY MAPLE SOFTWARE.

2019 ◽  
pp. 87
Author(s):  
Iļja Sučkovs ◽  
Aleksandrs Pikurs ◽  
Ilmārs Kangro
Keyword(s):  
Differential Equations ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
General Information ◽  
Radioactive Substance ◽  
Initial Value

With the passage of time and the development of technology, humanity is exploring new unknown problems that require complex analytical and numerical mathematical solutions. Due to their complexity differential equations are often used for this purpose. The aim of this work is to solve mathematical models of initial value problems of ordinary differential equations using the analitical method and numerical solution using MAPLE software. Also authors have provided general information about differential equations and diferent ways how they can be solved. As a result have been created two mathematical models which describe process of Determination of the cooling time of a shot animal and decomposition of the radioactive substance. Similar methods are also used to determine the age of objects as well

scholarly journals Numerical solution through mathematical modelling of unsteady MHD flow past a semi-infinite vertical moving plate with chemical reaction and radiation

2018 ◽  
Vol 40 (4) ◽  
pp. 270-281 ◽  
Author(s):  
Anupam Bhandari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Chemical Reaction ◽  
Mhd Flow ◽  
Time Dependent ◽  
Physical Parameters ◽  
Concentration Profiles ◽  
Partial Differential

Abstract In the present manuscript, unsteady magnetohydrodynamic (MHD) flow over a moving porous semi-infinite vertical plate with time-dependent suction has been studied in the presence of chemical reaction and radiation parameters. Time-dependent partial differential equations in the dimensionless form are solved numerically through mathematical modelling in COMSOL Multiphysics. The results are obtained for velocity, temperature and concentration profiles at different times. Steady state results are also presented for different values of physical parameters. The parameters involved in the problem are useful to change the characteristics of velocity, heat transfer and concentration profiles. The numerical solution of partial differential equations involved in the problem is obtained without sacrificing the relevant physical phenomena.

Optimum Design of Journal Bearings Dimensions for Rotating Machines

2020 ◽  
Vol 38 (10A) ◽  
pp. 1481-1488
Author(s):  
Tariq M. Hammza ◽  
Ehab N. Abas ◽  
Nassear R. Hmoad
Keyword(s):  
Aspect Ratio ◽  
Dynamic Response ◽  
Numerical Solution ◽  
Critical Speed ◽  
Design Method ◽  
Considerable Effect ◽  
Journal Bearings ◽  
Rotating Machines ◽  
Bearing Clearance ◽  
Study Results

The values of Many parameters which involve in the design of fluid film journal bearings mainly depend on the bearing applied load when using the conventional design method to design the journal bearings, in this study, as well as applied bearing load, the dynamic response and critical speed have been used to calculate the dimensions of journal bearings. In the field of rotating machine, especially a heavy-duty rotating machines, the critical speed and response are the main parameters that specify bearing dimensions. The bearing aspect ratio (bearing length to bore diameter) and bearing clearance have been determined based on rotor maximum critical speed and minimum response displacement. The analytical solution of rotor Eq. of motion was verified by numerical solution via using ANSYS Mechanical APDL 18.0 and by comparing the numerical solution with the preceding study. The final study results clearly showed that the bearing aspect ratio has little effect on the critical speed, but it has a high effect on the dynamic response also the bearing clearance has little effect on the critical speed and considerable effect on the dynamic response. The study showed that the more accurate values of bearing aspect ratio to make the response of rotor as low as possible are about 0.65 - 1 and bearing percent clearance is about 0.15 - 0.2 for different rotor dimensions.

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