scholarly journals The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Motions in Complex Plane

2017 ◽  
Vol 07 (03) ◽  
pp. 277-289
Author(s):  
Önder Sener ◽  
Ayhan Tutar
Keyword(s):  
Complex Plane ◽  
Moment Of Inertia ◽  
Polar Moment ◽  
Steiner Formula ◽  
Planar Motions

scholarly journals The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Homothetic Motions in Complex Plane

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Ayhan Tutar ◽  
Onder Sener
Keyword(s):  
Rotation Number ◽  
Complex Plane ◽  
Moment Of Inertia ◽  
Steiner Point ◽  
Control Panel ◽  
Area Formula ◽  
Polar Moment ◽  
Steiner Formula ◽  
Pole Point

The Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic motions in complex plane. The Steiner point or Steiner normal concepts were described according to whether rotation number was different from zero or equal to zero, respectively. The moving pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a winch was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of winch and the moving arm of winch. The results obtained in the second section of this study were applied for this motion.

Finding Principal Axes of Complex Plane Rigid Body with Rending-Image of MATLAB

2012 ◽  
Vol 490-495 ◽  
pp. 2156-2159
Author(s):  
Wu Gang Li
Keyword(s):  
Rigid Body ◽  
Complex Plane ◽  
Principal Axis ◽  
Flat Surface ◽  
Moment Of Inertia ◽  
Principal Axes ◽  
The Moment

In order to find the principal axes of inertia and calculate their moment of inertia to any plane homogeneous rigid body for calculating easily the moment of inertia to any axis of this rigid body, the principal axes could be found and their moment of inertia could be calculated automatically by using the reading-image of MATLAB to read the image messages about the flat surface of the rigid body and by the procedures which ware made according to the logic relation about the principal axis and the moment of inertia of the rigid body. Applying this method in a homogeneous cube, a result was acquired, error of which is small compared with the theoretical value. So this method is reliable, convenient and practical

Temporal variations of the polar moment of inertia and the second-degree geopotential

2004 ◽  
Vol 78 (3) ◽  
pp. 187-191 ◽  
Author(s):  
P. Varga ◽  
J. Engels ◽  
E.W. Grafarend
Keyword(s):  
Temporal Variations ◽  
Moment Of Inertia ◽  
Polar Moment ◽  
Second Degree

On the polar moment of inertia of a compressible body

1980 ◽  
Vol 22 (1) ◽  
pp. 57-60 ◽  
Author(s):  
J. Derral Mulholland
Keyword(s):  
Moment Of Inertia ◽  
Compressible Body ◽  
Polar Moment

Bobillier Formula for One Parameter Motions in the Complex Plane

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Soley Ersoy ◽  
Nurten Bayrak
Keyword(s):  
Complex Plane ◽  
Complex Number ◽  
Second Order ◽  
Geometrical Interpretation ◽  
Planar Motion ◽  
Radius Of Curvature ◽  
Fundamental Law ◽  
Planar Motions

This is a brief note expanding on the aspect of Fayet (2002, “Bobillier Formula as a Fundamental Law in Planar Motion,” Z. Angew. Math. Mech., 82(3), pp. 207–210), which investigates the Bobillier formula by considering the properties up to the second order planar motion. In this note, the complex number forms of the Euler Savary formula for the radius of curvature of the trajectory of a point in the moving complex plane during one parameter planar motion are taken into consideration and using the geometrical interpretation of the Euler Savary formula, Bobillier formula is established for one parameter planar motions in the complex plane. Moreover, a direct way is chosen to obtain Bobillier formula without using the Euler Savary formula in the complex plane. As a consequence, the Euler Savary given in the complex plane will appear as a particular case of Bobillier formula.

scholarly journals Rule-based equation for elastic tripping analysis of angle bar stiffeners

2012 ◽  
Vol 9 (2) ◽  
pp. 103-111 ◽  
Author(s):  
Ahmad Rahbar Ranji
Keyword(s):  
Energy Method ◽  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Beam Theory ◽  
Moment Of Inertia ◽  
Rule Base ◽  
Rule Based ◽  
Buckling Modes ◽  
Polar Moment ◽  
Marine Engineering

Tripping is one of buckling modes in stiffened plates which could be occurred in the stiffeners with high flexural rigidity and low torsional rigidity. Rule-base expressions for calculation of sectorial moment of inertia of angle-bar stiffeners are scattered. An expression for calculation of sectorial moment of inertia of angle-bar stiffeners is derived based on energy method and beam theory. Sectorial moment of inertia of different angle-bar stiffeners are calculated and compared with the values calculated by different classification society rules. It is found that some of the rule-based equations for calculation of sectorial moment of inertia of angle-bar stiffeners are inaccurate. Euler tripping stress of different angle bars are calculated by energy method and compared with rule-based equation and finite element method. It is found that, rule-based expression for calculation of polar moment of inertia of angle-bar stiffeners neglects one term, which could lead up to 10% overestimation of Euler tripping stress. DOI: http://dx.doi.org/10.3329/jname.v9i2.10443 Journal of Naval Architecture and Marine Engineering 9(2012) 105-111

Development of a Small Mixed-Flow Turbine for Automotive Turbochargers

1995 ◽  
Author(s):  
Hiroaki Minegishi ◽  
Hiromi Matsushita ◽  
Masaru Sakakida ◽  
Takaaki Koike
Keyword(s):  
Small Diameter ◽  
Turbine Rotor ◽  
Moment Of Inertia ◽  
Light Weight ◽  
Passenger Cars ◽  
Mixed Flow ◽  
Inertia Moment ◽  
Passenger Car ◽  
Radial Turbine ◽  
Polar Moment

In recent years, turbocharging technologies for passenger cars have progressed significantly. However, “Turbo Lag” is still one of the most important problems in turbocharging technologies. In order to improve response to acceleration, it is effective to reduce the polar moment of inertia of rotating parts. The turbine rotor designed with small diameter, light weight and high specific-speed contributes toward reducing inertia moment of the rotating parts. The further request for the smaller moment of inertia for passenger car applications made it difficult to satisfy the request with a conventional radial turbine rotor. This is why we developed a mixed-flow turbine rotor. This paper explains the computer analysis we carried out and experimental test data of the mixed-flow turbine for passenger car applications.

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