The theory of longitudinal vibrations of a conical elastic body in an elastic medium

2016 ◽  
Vol 3 (1) ◽  
pp. 27-35
Author(s):  
V. Bulgakov ◽  
V. Adamchuk ◽  
I. Holovach ◽  
D. Orszaghova
Keyword(s):  
Elastic Medium ◽  
Elastic Body ◽  
Cross Sections ◽  
Ritz Method ◽  
Frequency Equation ◽  
The Body ◽  
Longitudinal Vibrations ◽  
Beet Root ◽  
Analytic Expressions ◽  
Stationary Action

Aim. To elaborate the theory of longitudinal vibrations of a solid elastic body with one fi xed end in the elastic medium. The example of such a body may be found in a sugar beet root in soil, the latter being elastic medium. Methods. The principle of stationary action of Ostrogradsky-Hamilton and the Ritz method were applied in the work. Results. The Ritz method was applied to obtain the Ritz frequency equation for the oscillating process under investigation. The analytic expressions were defi ned to determine the fi rst and second eigenfrequencies of vibration and the amplitude of constrained vibrations of any of its cross-sections. The values of the fi rst and second eigenfrequencies of the elastic body under investigation with specifi c geometric and physical pa- rameters were found. The dependency diagrams for the fi rst and second eigenfrequencies on the coeffi cient of elastic contraction of soil as the elastic medium, and the dependency diagrams for the amplitude of constrained oscillations of the mentioned body on the coeffi cient c of elastic deformation of soil and the distance of the cross-section of the body from the conditional point of fi xation were drawn. The dependency diagrams for the amplitude of constrained oscillations of the elastic body on the change in the amplitude and the frequency of perturbing force were obtained. Conclusions. The impossibility of resonance occurrence was substantiated as the frequency of the perturbing force cannot equal the frequency of eigenvibrations of the elastic body due to technological and technical reasons. It was proven that the breaking of the elastic body is impossible with lon- gitudinal deformations due to the shortness of the amplitude of longitudinal vibrations of the mentioned body.

Three-Dimensional Vibration Analysis of a Truncated Quadrangular Pyramid

1987 ◽  
Vol 54 (1) ◽  
pp. 115-120 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Tagawa
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Frequency Equation ◽  
The Body ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Transformation Of Variables ◽  
Unit Edge

An analysis is presented for the three-dimensional vibration problem of determining the natural frequencies and the mode shapes of a truncated quadrangular pyramid. For this purpose, the body is transformed into a right quadrangular prism with unit edge lengths by a transformation of variables. With the displacements of the transformed prism assumed in the forms of algebraic polynomials, the dynamical energies of the prism are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to quadrangular pyramids in which the base is clamped and the other sides are free, and the natural frequencies (the eigenvalues of vibration) and the mode shapes are calculated numerically, from which the vibration characteristics arising in the pyramids are studied.

Gender determination of caucasoid hair using image analysis

1993 ◽  
Vol 51 ◽  
pp. 216-217
Author(s):  
T.B. Ball ◽  
W.M. Hess
Keyword(s):  
Image Analysis ◽  
Cross Sections ◽  
Scalp Hair ◽  
The Body ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Hair Samples ◽  
Length Width ◽  
Morphological Differences

It has been demonstrated that cross sections of bundles of hair can be effectively studied using image analysis. These studies can help to elucidate morphological differences of hair from one region of the body to another. The purpose of the present investigation was to use image analysis to determine whether morphological differences could be demonstrated between male and female human Caucasian terminal scalp hair.Hair samples were taken from the back of the head from 18 caucasoid males and 13 caucasoid females (Figs. 1-2). Bundles of 50 hairs were processed for cross-sectional examination and then analyzed using Prism Image Analysis software on a Macintosh llci computer. Twenty morphological parameters of size and shape were evaluated for each hair cross-section. The size parameters evaluated were area, convex area, perimeter, convex perimeter, length, breadth, fiber length, width, equivalent diameter, and inscribed radius. The shape parameters considered were formfactor, roundness, convexity, solidity, compactness, aspect ratio, elongation, curl, and fractal dimension.

Measurements of turbulent crossflow separation created by a curved body of revolution

2007 ◽  
Vol 589 ◽  
pp. 353-374 ◽  
Author(s):  
P. A. GREGORY ◽  
P. N. JOUBERT ◽  
M. S. CHONG
Keyword(s):  
Flow Visualization ◽  
Skin Friction ◽  
Cross Sections ◽  
Separated Flow ◽  
Surface Flow ◽  
The Body ◽  
Body Of Revolution ◽  
Outer Flow ◽  
Friction Measurements ◽  
Surface Flow Visualization

Using the method pioneered by Gurzhienko (1934), the crossflow separation produced by a body of revolution in a steady turn is examined using a stationary deformed body placed in a wind tunnel. The body of revolution was deformed about a radius equal to three times the body's length. Surface pressure and skin-friction measurements revealed regions of separated flow occurring over the rear of the model. Extensive surface flow visualization showed the presence of separated flow bounded by a separation and reattachment line. This region of separated flow began just beyond the midpoint of the length of the body, which was consistent with the skin-friction data. Extensive turbulence measurements were performed at four cross-sections through the wake including two stations located beyond the length of the model. These measurements revealed the location of the off-body vortex, the levels of turbulent kinetic energy within the shear layer producing the off-body vorticity and the large values of 〈uw〉 stress within the wake. Velocity spectra measurements taken at several points in the wake show evidence of the inertial sublayer. Finally, surface flow topologies and outer-flow topologies are suggested based on the results of the surface flow visualization.

Comparison of Static and Dynamic Stiffness for Beams Undergoing Flexural and Torsional Loading With an Intermediate Mass

2000 ◽  
Author(s):  
Arnoldo Garcia ◽  
Arnold Lumsdaine ◽  
Ying X. Yao
Keyword(s):  
Closed Form ◽  
Natural Frequency ◽  
Cross Sections ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Frequency Equation ◽  
Form Solution ◽  
Torsional Loading ◽  
Intermediate Mass ◽  
Form Equation

Abstract Many studies have been performed to analyze the natural frequency of beams undergoing both flexural and torsional loading. For example, Adam (1999) analyzed a beam with open cross-sections under forced vibration. Although the exact natural frequency equation is available in literature (Lumsdaine et al), to the authors’ knowledge, a beam with an intermediate mass and support has not been considered. The models are then compared with an approximate closed form solution for the natural frequency. The closed form equation is developed using energy methods. Results show that the closed form equation is within 2% percent when compared to the transcendental natural frequency equation.

On the Motion of an Elastic Body Rolling/Sliding on an Elastic Substrate

1995 ◽  
Vol 117 (2) ◽  
pp. 308-314 ◽  
Author(s):  
A. Spector ◽  
R. C. Batra
Keyword(s):  
Elastic Body ◽  
Frictional Force ◽  
Three Dimensional ◽  
The Body ◽  
Elastic Substrate ◽  
Linear Elastic ◽  
Linear Elastic Body ◽  
Body Rolling ◽  
Applied Forces ◽  
Two Phases

The three-dimensional evolutionary problem of rolling/sliding of a linear elastic body on a linear elastic substrate is studied. The inertial properties of the body regarded as rigid are accounted for. By employing an asymptotic analysis, it is shown that the process can be divided into two phases: transient and quasistationary. An expression for the frictional force as a function of the externally applied forces and moments, and inertial properties of the body is derived. For an ellipsoid rolling/sliding on a linear elastic substrate, numerical results for the frictional force distribution, slip/adhesion subareas, and the evolution of the slip velocity are given.

Long bone cross-sectional geometry

2020 ◽  
pp. 307-320
Author(s):  
Christopher B. Ruff ◽  
Ryan W. Higgins ◽  
Kristian J. Carlson
Keyword(s):  
Mechanical Properties ◽  
Cross Sections ◽  
Lateral Displacement ◽  
Center Of Mass ◽  
Gait Pattern ◽  
Locomotor Behavior ◽  
The Body ◽  
Long Bone ◽  
Cross Sectional ◽  
Body Center

Long bone diaphyseal cross-sectional geometries reflect the mechanical properties of the bones, and can be used to aid in inferences of locomotor behavior in extinct hominins. This chapter considers all available long bone diaphyseal and femoral neck cross-sections of specimens from Sterkfontein Member 4, and presents comparisons of these section properties and other cross-sectional dimensions with those of other early hominins as well as modern samples. The cross-sectional geometry of the Sterkfontein Member 4 long bone specimens suggests some similarities to, but also interesting differences in, mechanical loading of these elements relative to modern humans. The less asymmetric cortical bone distribution in the Sterkfontein femoral necks is consistent with other evidence above indicating an altered gait pattern involving lateral displacement of the body center of mass over the stance limb. The relatively very strong upper limb of StW 431 implies that arboreal behavior formed a significant component of its locomotor repertoire. Bipedal gait may have been less efficient and arboreal climbing more prevalent in the Sterkfontein hominins.

scholarly journals Charge-exchange and energy-loss statistics of swift penetrating ions

1995 ◽  
Vol 13 (2) ◽  
pp. 281-292 ◽  
Author(s):  
P. Sigmund ◽  
A. Närmann
Keyword(s):  
Energy Loss ◽  
Charge State ◽  
Charge Exchange ◽  
Cross Sections ◽  
Adequate Description ◽  
Direct Evaluation ◽  
Experimental Parameters ◽  
Analytic Expressions ◽  
Input Side ◽  
Exchange Options

A general and powerful formalism has been developed for computation of energy-loss spectra of penetrating charged particles in the presence of charge exchange. Options on the input side are the cross sections for electron capture and loss, transition rates for radiative and nonradiative spontaneous processes and their associated energy losses or gains, and finally, cross sections for all processes that contribute to particle stopping but are not associated with charge exchange. The formalism generates an n × n transfer matrix, where n is the number of states needed for an adequate description of the projectile under consideration. This matrix delivers the joint distribution of energy loss and exit charge state for a given incident charge state and energy.The formalism can be used in principle as an alternative for Monte Carlo simulation, but until now we have concentrated on direct evaluation of key experimental parameters related to the energy-loss spectrum integrated over all exit charge states, in particular, mean energy loss, straggling, and skewness. Generally, valid analytic expressions have been found for these quantities, each of which can be separated into a stationary term representing chargestate equilibrium and a transient depending on the incident charge state. A brief survey is given of current analytic and numerical efforts addressing other experimental parameters.

scholarly journals Swimming Turned on Its Head: Stability and Maneuverability of the Shrimpfish (Aeoliscus punctulatus)

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
F E Fish ◽  
R Holzman
Keyword(s):  
Cross Sections ◽  
Swimming Performance ◽  
Center Of Mass ◽  
Leading Edge ◽  
Longitudinal Axis ◽  
The Body ◽  
Maximum Speed ◽  
Vertical Orientation ◽  
Neutrally Buoyant ◽  
Orientation Modification

Synopsis The typical orientation of a neutrally buoyant fish is with the venter down and the head pointed anteriorly with a horizontally oriented body. However, various advanced teleosts will reorient the body vertically for feeding, concealment, or prehension. The shrimpfish (Aeoliscus punctulatus) maintains a vertical orientation with the head pointed downward. This posture is maintained by use of the beating fins as the position of the center of buoyancy nearly corresponds to the center of mass. The shrimpfish swims with dorsum of the body moving anteriorly. The cross-sections of the body have a fusiform design with a rounded leading edge at the dorsum and tapering trailing edge at the venter. The median fins (dorsal, caudal, anal) are positioned along the venter of the body and are beat or used as a passive rudder to effect movement of the body in concert with active movements of pectoral fins. Burst swimming and turning maneuvers by yawing were recorded at 500 frames/s. The maximum burst speed was 2.3 body lengths/s, but when measured with respect to the body orientation, the maximum speed was 14.1 body depths/s. The maximum turning rate by yawing about the longitudinal axis was 957.5 degrees/s. Such swimming performance is in line with fishes with a typical orientation. Modification of the design of the body and position of the fins allows the shrimpfish to effectively swim in the head-down orientation.

scholarly journals The most complex theory of the symmetric impact of the vibrating digging working tool on the sugar beet root

2018 ◽  
Vol 49 (4) ◽  
pp. 207-219
Author(s):  
Volodymyr Bulgakov ◽  
Hristo Beloev ◽  
Ivan Holovach ◽  
Vladimir Kročko ◽  
Ladislav Nozdrovicky ◽  
...  
Keyword(s):  
Sugar Beet ◽  
Structural Parameters ◽  
Experimental Studies ◽  
The Body ◽  
Refined Theory ◽  
Beet Root ◽  
Impact Interaction ◽  
Solid Soil ◽  
Sugar Beet Root ◽  
Theoretical Mechanics

When digging sugar beet root out of the soil by using a vibration digging working tools, there occur impact contacts of the working tools and sugar beet roots placed in the soil. Such phenomena are formed mainly in conditions of dry and solid soil. The consequence of this is a significant impact contact tails breaks, chips or damage of the side surfaces of roots, which leads ultimately to a non-return losses on sugar mass. Therefore there is a need to develop the basic provisions of the refined theory of impact interaction of a vibrating digging working tool with the body of the sugar beet root fixed in the soil, and on the basis of the results obtained to justify rational kinematic and structural parameters of advanced vibration digging working tool. Within the research there was used the methods of higher mathematics, theoretical mechanics, programming and numerical calculations on the PC. We have developed a refined theory of impact interaction of digging of the working body of the sugar beet harvester with the body of sugar beet root during vibratory digging of sugar beet roots from the dry and solid soil. On the basis of obtained equations and their numerical solution by PC programme it was possible to define the kinematic and structural parameters of vibration digging working tool that will ensure the conditions not to damage or break the tails of the sugar beet roots during their digging out from the dry and solid soil. We have investigated the so-called symmetric impact of the vibrating digging working body and the body of sugar beet root. As shown by calculations of the obtained theoretical dependencies and confirmed experimental studies, for the range of reduced masses of the vibrating excavating organ 0.8-2.0 kg, the translational velocity 1.3-2.2 m∙s–1, the depth in the soil 0.08-0.12 m and the vibration amplitude 0.008-0.024 m for shock interaction, which is most likely in dry and solid soil, the permissible oscillation frequency of scooping coulter is 10.0-18.0 Hz.

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