scholarly journals Properties of inertia of a solid body

2020 ◽  
pp. 33-37
Author(s):  
T.B. Goldvarg ◽  
◽  
V.N. Shapovalov ◽  
Keyword(s):  
Solid Body ◽  
Geometric Approach ◽  
The Body ◽  
Geometric Symmetry

Definitions are given and properties of inertial characteristics of solid are formulated; the influence of geometric symmetry of the body on its characteristics is described. The geometric approach to the presentation of the material is used.

A Method for Tracking a Solid Body in a Fluid Field in Immersed Boundary Methods

2018 ◽  
Author(s):  
Guangfa Yao
Keyword(s):  
Level Set ◽  
Solid Body ◽  
Volume Fraction ◽  
Transformation Matrix ◽  
The Body ◽  
New Method ◽  
Immersed Boundary ◽  
Body Interaction ◽  
Level Set Function ◽  
Set Function

Immersed boundary method has got increasing attention in modeling fluid-solid body interaction using computational fluid dynamics due to its robustness and simplicity. It usually simulates fluid-solid body interaction by adding a body force in the momentum equation. This eliminates the body conforming mesh generation that frequently requires a very labor-intensive and challenging task. But accurately tracking an arbitrary solid body is required to simulate most real world problems. In this paper, a few methods that are used to track a rigid solid body in a fluid domain are briefly reviewed. A new method is presented to track an arbitrary rigid solid body by solving a transformation matrix and identifying it using a level set function. Knowing level set function, the solid volume fraction can be derived if needed. A three-dimensional example is used to study a few methods used to represent and solve the transformation matrix, and demonstrate the presented new method.

Unsteady Conduction in a Horizontal Solid Cylinder Cooled by Natural Convection: Alternate Lumped Criterion in Terms of the Solid Material

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Antonio Campo ◽  
Jaime Sieres
Keyword(s):  
Thermal Conductivity ◽  
Natural Convection ◽  
Heat Exchange ◽  
Solid Body ◽  
Biot Number ◽  
The Body ◽  
Convection Heat ◽  
Lumped Model ◽  
Convective Coefficient ◽  
The Mean

Within the framework of the potent lumped model, unsteady heat conduction takes place in a solid body whose space–mean temperature varies with time. Conceptually, the lumped model subscribes to the notion that the external convective resistance at the body surface dominates the internal conductive resistance inside the body. For forced convection heat exchange between a solid body and a neighboring fluid, the criterion entails to the lumped Biot number Bil=(h¯/ks)(V/A)<0.1, in which the mean convective coefficient h¯ depends on the impressed fluid velocity. However, for natural convection heat exchange between a solid body and a fluid, the mean convective coefficient h¯ depends on the solid-to-fluid temperature difference. As a consequence, the lumped Biot number must be modified to read Bil=(h¯max/ks)(V/A)<0.1, wherein h¯max occurs at the initial temperature Ti for cooling or at a future temperature Tfut for heating. In this paper, the equivalence of the lumped Biot number criterion is deduced from the standpoint of the solid thermal conductivity through the solid-to-fluid thermal conductivity ratio.

On the equations of rotation of a solid body about a fixed point

1864 ◽  
Vol 13 ◽  
pp. 52-64
Keyword(s):  
Fixed Point ◽  
Solid Body ◽  
The Body ◽  
Principal Axes ◽  
Usual Notation

In treating the equations of rotation of a solid body about a fixed point, it is usual to employ the principal axes of the body as the moving system of coordinates. Cases, however, occur in which it is advisable to employ other systems; and the object of the present paper is to develope the fundamental formulæ of transformation and integration for any system. Adopting the usual notation in all respects, excepting a change of sign in the quantities F, G, H, which will facilitate transformations hereafter to be made, let A = Σ m ( y 2 + z 2 ), B = Σ m ( z 2 + x 2 ), C= Σ m ( x 2 + y 2 ), -F = Σ myz , -G = Σ mzx , -H = Σ mxy ;

Blunt-body impact on the free surface of a compressible liquid

1994 ◽  
Vol 263 ◽  
pp. 319-342 ◽  
Author(s):  
Alexander Korobkin
Keyword(s):  
Free Surface ◽  
Solid Body ◽  
Contact Point ◽  
Single Point ◽  
Fluid Motion ◽  
Nonlinear Problems ◽  
Compressible Liquid ◽  
The Body ◽  
Expansion Waves ◽  
Acoustic Approximation

The present paper deals with the plane unsteady problem of the penetration of a blunt solid contour into an ideal compressible liquid. At the initial instant of time, the solid body touches the liquid free boundary at a single point. At the initial stage, the duration of which depends on the body geometry, the displacements of liquid particles are small and the disturbed fluid motion is described within the framework of the acoustic approximation. The main feature of the problem is the existence of a contact line between the free surface of the liquid and the solid-body surface. The position of this line is not known in advance and is to be determined together with the solution of the problem. A brief description of the method that provides a solution of complicated nonlinear problems such as this is given. The pressure distribution and the velocity field in the liquid are shown to be given in quadratures and in the case of a parabolic entering contour in an explicit form. For a parabolic entering contour the pressure at the top of the contour calculated using the model of an incompressible liquid is observed to deviate from a precise value by not more than 10% of the latter after the first expansion waves have passed the contact point. The solution analysis enabled us to distinguish the regions in which the acoustic approximation fails and the liquid flow becomes essentially nonlinear.

Note on hydrodynamics

1953 ◽  
Vol 49 (2) ◽  
pp. 342-354 ◽  
Author(s):  
Charles Darwin
Keyword(s):  
Kinetic Energy ◽  
Incompressible Fluid ◽  
Solid Body ◽  
The Body ◽  
Mechanics Of Fluids ◽  
General Mechanics ◽  
Rotating Body ◽  
Real Fluid ◽  
Fluid Particles

AbstractA study is made of the actual trajectories of fluid particles in certain motions of classical hydrodynamics. When a solid body moves through an incompressible fluid, it induces a drift in the fluid, such that the final positions of the particles are further on than those from which they started. The drift-volume enclosed between the initial and final positions is equal to the volume corresponding to hydrodynamic mass, that is, the mass of fluid to be added to that of the solid in calculating its kinetic energy. This result is proved quite generally. The work involves integrals which are not absolutely convergent, and these are discussed in relation to the general mechanics of fluids. When the trajectories are considered of the fluid surrounding a rotating body, it is shown that the fluid particles slowly drift round the body, even though the motion is irrotational and without circulation. There seems to be in some respects a closer resemblance between the behaviour of the idealized hydrodynamic fluid and a real fluid than might be expected from the well-known discrepancies between them.

scholarly journals Comparison of the Vibration Damping of the Wood Species Used for the Body of an Electric Guitar on the Vibration Response of Open-Strings

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5281
Author(s):  
Tony Ray ◽  
Jasmin Kaljun ◽  
Aleš Straže
Keyword(s):  
Solid Body ◽  
Coupling Effect ◽  
Juglans Regia ◽  
Vibration Damping ◽  
The Body ◽  
Electric Guitar ◽  
Open Strings ◽  
Radiated Sound ◽  
Positive Effect ◽  
Research Show

Research show that the vibrations of the strings and the radiated sound of the solid body electric guitar depend on the vibrational behavior of its structure in addition to the extended electronic chain. In this regard, most studies focused on the vibro-mechanical properties of the neck of the electric guitar and neglected the coupling of the vibrating strings with the neck and the solid body of the instrument. Therefore, the aim of the study was to understand how the material properties of the solid body could affect the stiffness and vibration damping of the whole instrument when comparing ash (Fraxinus excelsior L.) and walnut (Juglans regia L.) wood. In the electric guitar with identical components, higher modal frequencies were confirmed in the structure of the instrument when the solid body was made of the stiffer ash wood. The use of ash wood for the solid body of the instrument due to coupling effect resulted in a beneficial reduction in the vibration damping of the neck of the guitar. The positive effect of the low damping of the solid body of the electric guitar made of ash wood was also confirmed in the vibration of the open strings. In the specific case of free-free vibration mode, the decay time was longer for higher harmonics of the E2, A2 and D3 strings.

scholarly journals AN INVESTIGATION OF THE SILHOUETTES OF CHRISTIAN DIOR

2019 ◽  
Vol 7 (3) ◽  
pp. 167-178
Author(s):  
Krasimira Radieva
Keyword(s):  
Human Body ◽  
Geometric Approach ◽  
The Body ◽  
Body Form ◽  
Fashion Designers

The variety of silhouettes is one of main features of Christian Dior’s creativity. The aim of presented paper is a study and analysis of the silhouettes of Christian Dior for determination of connection between a silhouette and the body form and presentation of a silhouette with simple geometric forms. The silhouettes of Christian Dior in his couture collections in the period between 1947 and 1957 are studied, analysed and approximated with combination of well-known simple geometric forms - curved forms of ellipses, ovals, circles, full figures or their parts, and straight ones of rectangles and trapeziums. The investigation of the silhouettes with the application of approximation with well-known simple geometric forms helps the students in their studies in fashion. The approximated geometric approach helps the activity of fashion designers and pattern makers in their creations of new silhouette forms and their proportions to the human body.

Fuzzy Logic-based Techniques for Motion Planning of a Robot Manipulator Amongst Unknown Moving Obstacles

Robotica ◽  
1992 ◽  
Vol 10 (6) ◽  
pp. 563-574 ◽  
Author(s):  
Anupam Bagchi ◽  
Himanshu Hatwal
Keyword(s):  
Motion Planning ◽  
Fuzzy Controller ◽  
Robot Manipulator ◽  
Dynamic Environment ◽  
Geometric Approach ◽  
The Body ◽  
Sensory Data ◽  
Revolute Joints ◽  
Manipulator Link ◽  
Kinematic Motion

SUMMARYAn algorithm for kinematic motion planning of redundant planar robots, having revolute joints, in an unknown dynamic environment is presented. Distance ranging sensors, mounted on the body of each manipulator link, are simulated here to estimate the proximity of an obstacle. The sensory data is analyzed through a fuzzy controller which estimates whether a collision is imminent, and if so, employs a geometric approach to compute the joint movements necessary to avoid the collision. Obstacles can sometimes move uncompromisingly in the environment attempting a deliberate collision. Strategies to deal with such cases are presented and recovery procedures to circumvent the obstacle from tight corners are suggested. Cases of link overlap have been avoided by considering each link as a body which is sensed as an obstacle by every other link of the same manipulator. Suitable examples are presented to demonstrate the algorithm.

On Math Modeling of Solid Body’s Motion Control with an Excess Number of Rope Propulsion Devices

2019 ◽  
Vol 20 (7) ◽  
pp. 422-427
Author(s):  
E. S. Briskin ◽  
V. N. Platonov
Keyword(s):  
Mathematical Model ◽  
Solid Body ◽  
Translational Motion ◽  
The Body ◽  
Switching Frequency ◽  
Anchor Cable ◽  
Dc Motors ◽  
Control Actions ◽  
Stepper Motors ◽  
The Mathematical Model

A design scheme and a mathematical model of the dynamics of the translational motion of a solid body, which simulate the movement of an underwater platform using anchor-cable propulsion devices, are proposed, and examples of the use of such platforms during the mining and exploration of new hydrocarbon deposits on the continental shelf are given. A diagram of the underwater platform with anchor-cable propulsion devices, as well as the method of its movement. The peculiarity of the mathematical model of the process of moving a platform with this type of propulsion devices is in the dependence of the developed efforts on the position of the cables relative to the moving body and the excess of the number of control actions over the number of degrees of freedom of the mechanical system. The mathematical model describing the movement of the platform is based on geometric equations with simultaneous operation of propulsion drives on the one hand, and on the equation of the dynamics of the translational motion of the body on the other. It is shown that the task of the control system in this process is to provide the necessary balance of forces in the cables going to the propulsion anchor. As drives, DC motors and stepper motors are considered due to their ability to operate from an independent power source, such as batteries. The features of control of DC motors and stepper motors as part of anchor-cable drives drives are established. To resolve dynamic uncertainty, the necessity of introducing an additional equation into a mathematical model has been proved. In accordance with the developed mathematical model, the laws of changes in time of control actions are obtained, in particular, such as the voltage applied to the armatures of DC motors and the switching frequency of the windings when using stepping motors. A method for controlling the movement of a solid body under the influence of two drives has been developed. It can be used to study the translational movement of an underwater platform with anchor-cable propulsion devices. The features of control of DC motors and stepper motors are considered to change the length of cable drives according to a given law.

Lunar ranging experiment ephemerides and the reduction of observations (summary only)

1977 ◽  
Vol 284 (1326) ◽  
pp. 467-467
Keyword(s):  
Solid Body ◽  
Equations Of Motion ◽  
The Body ◽  
Lunar Orbit ◽  
Earth Tides ◽  
Lunar Laser Ranging ◽  
Fitting Procedure ◽  
The Earth ◽  
Starting Conditions ◽  
Tesseral Harmonics

The generation of a lunar laser ranging ephemeris uses numerical integrations of the lunar orbit and physical librations and a data fitting procedure. The relativistic equations of motion for the nine planets and the Moon are simultaneously integrated with perturbations on the lunar orbit from zonal harmonics of the Earth through degree four, lunar tesseral harmonics through degree and order three, and a tidal bulge on the Earth. The integration of the lunar rotation follows from the torques of the Earth and Sun on a solid body Moon with gravitational harmonics through degree and order three. The fitting program utilizes the integrations of the orbit and physical librations, nominal values of U.T. 1 and polar motion from the Bureau International de l’Heure, and includes corrections for atmospheric delays, nutations of the Earth’s pole taken to the body axis, solid body Earth tides, monthly and bimonthly tidal corrections in U. T. 1, and relativistic clock transformations. Not only do the fits give new starting conditions for the orbit and libration integrations but improved observatory and retroreflector coordinates, the mass ratio Sun/(Earth + Moon), and harmonics of the lunar gravity field.

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