scholarly journals RESEARCH OF VIBROREOLOGICAL MODELS OF LAYER OF BULK ENVIRONMENT

2021 ◽  
pp. 60-69
Author(s):  
Yurii Polievoda ◽  
Yevhenii Volynets
Keyword(s):  
Approximate Solution ◽  
Dry Friction ◽  
Viscous Friction ◽  
Slow Motion ◽  
The Body ◽  
Free Medium ◽  
Medium Layer ◽  
Bulk Medium ◽  
Slow Motions ◽  
Complex Cases

Vibration mechanics and vibroreology play an important role in the new section of applied vibration theory formed in recent years - the theory of vibration processes and devices. This theory studies the patterns of excitation and vibration in different mechanical systems; it also includes the theory of machines in which vibration is used to achieve useful goals. Based on the considered models, it was possible to describe the chaotic motion of the bulk medium layer over the vibrating plane. Such movements, well known for liquids, have indeed been observed in the case of a bulk medium, which serves as another confirmation of the possibility of modeling slow motions of a bulk medium during vibration in the form of viscous fluid motions (of course, with the above caveats and additions). When studying the described simplest models, motion (including we are interested in slow motion) can be found by directly using the solution of the problem of vibrotransportation of the body (particles). The value of this approach is determined, however, by the possibility of its application for an approximate solution in more complex cases. In the study of slow motions of bodies interacting with both the forces of dry friction and collisions, these interactions can be modeled by the forces of viscous friction, taking into account the driving vibration force. This leads to the following vibroreological approach to modeling the behavior of the bulk medium in vibrating trays and vessels. Of all the considered models, the most promising is the model of the behavior of the bulk medium under the influence of vibration in the form of a viscous medium.The described models can be used when considering a practically important task of vibration penetration into a free medium.

scholarly journals On rolling friction

2019 ◽  
Vol 485 (3) ◽  
pp. 295-299
Author(s):  
A. P. Ivanov
Keyword(s):  
Friction Coefficient ◽  
Angular Velocity ◽  
Viscous Friction ◽  
Rolling Friction ◽  
The Body ◽  
Normal Velocity ◽  
Contact Conditions ◽  
Combined Motion ◽  
Pure Rolling ◽  
Over Time

The dependence of rolling friction on velocity for various contact conditions is discussed. The principal difference between rolling and other types of relative motion (sliding and spinning) is that the points of the body in contact with the support change over time. Due to deformations, there is a small contact area and, entering into contact, the body points have a normal velocity proportional to the diameter of this area. For describing the dependence of the friction coefficient on the angular velocity in the case of “pure” rolling, a linear dependence is proposed that admits a logical explanation and experimental verification. Under the combined motion, the rolling friction retains its properties, the sliding and spinning friction acquiring the properties of viscous friction.

Slow Motions of A Circular Cylinder in a Liquid after a Separation Impact

2021 ◽  
pp. 16-21
Author(s):  
Michail V. Norkin
Keyword(s):  
Circular Cylinder ◽  
Small Parameter ◽  
Asymptotic Approximation ◽  
The Body ◽  
Square Root ◽  
Ship Hydrodynamics ◽  
A Value ◽  
Slow Motions ◽  
Acceleration Of Gravity ◽  
The Impact

The plane problem of the separation impact of a circular cylinder completely immersed in an ideal incompressible heavy liquid is considered. It is assumed that after the impact, the cylinder moves horizontally at a constant speed. An attached cavity is formed behind the body, the shape of which depends on the physical and geometric parameters of the problem. It is required to study the process of collapse of the cavity at low velocities of the cylinder, which correspond to small Froude numbers. The solution to the problem is constructed using asymptotic expansions in a small parameter, which is the dimensionless speed of the cylinder. In this case, as the characteristic speed of the problem, a value is chosen equal to the square root of the product of the radius of the cylinder and the acceleration of gravity. As a result of this choice, the indicated small parameter coincides with the Froude number, and therefore, we can assume that the asymptotics of the problem is constructed for small Froude numbers. In the leading asymptotic approximation, a mixed problem of potential theory with one-sided constraints on the surface of the body is formulated. With its help, the position of the separation points at each moment of time is determined and the time of collapse of a thin cavity is found. The results obtained can be used to solve practical problems of ship hydrodynamics, in which it is necessary to take into account the phenomenon of cavitation.

Modeling and Analysis of a Ball and Beam System Including Impacts and Dry Friction

2014 ◽  
Author(s):  
Diego Colón ◽  
Átila Madureira Bueno ◽  
Ivando S. Diniz ◽  
Jose M. Balthazar
Keyword(s):  
Differential Inclusion ◽  
Dry Friction ◽  
Viscous Friction ◽  
Mathematical Object ◽  
Contact Forces ◽  
Modeling And Analysis ◽  
Typical Situation ◽  
Beam System ◽  
The Impact ◽  
Ball And Beam System

The Ball and Beam system is a common didactical plant that presents a complex nonlinear dynamics. This comes from the fact that the ball rolls over the beam, which rotates around its barycenter. In order to deduce the system’s equations, composition of movement must be applied, using a non-inertial reference frame attached to the beam. In the Literature, a common hypothesis is to suppose that the ball rolls without slipping. If a viscous friction is supposed to be present, a simpler situation is obtained, where Lagrangean mechanics can be applied, and no contact force is known. Even then, the dynamics is very nonlinear. However, this model does not include all the relevant phenomena, such as ball’s slipping at higher beam’s inclination angles, dry friction between the ball and the beam, and impacts between: 1) the ball and the ends of the beam, and 2) the beam and the base (ground). These additions to the model impose the necessity to calculate, in a simulation setting, the contact forces, and the Newton’s approach to determine the system’s equations becomes more convenient. Also, discontinuities in the model are introduced, and the simpler mathematical object for model such systems are the differential inclusion systems. In this work, we deduce the Ball and Beam differential inclusion system, including dry friction and the impact between the ball and beam. We also present simulation results for the corresponding differential inclusion system in a typical situation.

The Structure Design of Gait Pole Climbing Robot

2015 ◽  
Vol 740 ◽  
pp. 171-174
Author(s):  
Xiao Jin Fu ◽  
Zhao Yang Sun ◽  
Ran Zhao ◽  
Jian Cheng Yin
Keyword(s):  
Slow Motion ◽  
Structure Design ◽  
The Body ◽  
Industrial Robots ◽  
Climbing Robot ◽  
Climbing Robots ◽  
Robot Arms ◽  
Maintenance Work ◽  
Industrial Software

The theory of gait is one of walking ways which is efficient, fast and stable in a variety of industrial robots, offering a structure of climbing robots in a way of gait and climbing with the gait motion in paper. Through the results of analysis by various industrial software, the presented structure of climbing robots which is composed of two terminal parts and two robot arms that is the part of pedestal and climbing mechanism. In the process of climbing, realizing gripping, Swing work, turning work, an orderly motion and get to the aimed place finally through alternate between the upper and lower part of the body by the control of SCM. The presented method has not only improved many problems like complicated climbing structure, controlling rough, slow-motion and unable thronging obstacles, but also accomplished the subsequent operations like tools delivering, pole testing, clearing, maintenance work, furthermore, there has more comprehensive benefits.

Biology and physics of locust flight. III. The aerodynamics of locust flight

1956 ◽  
Vol 239 (667) ◽  
pp. 511-552 ◽  
Keyword(s):  
Body Weight ◽  
Posterior Part ◽  
Slow Motion ◽  
Middle Part ◽  
The Body ◽  
Vertical Force ◽  
Aerodynamic Forces ◽  
Locust Flight ◽  
Lift And Drag ◽  
Wing Stroke

A proper understanding of how locusts fly must be based upon knowledge of how the wings are moved. A desert locust was suspended from a balance and placed in an air stream so that it flew under nearly the same conditions as during natural forward flight. Four stroboscopic slow-motion films were selected for measurement. The movements of the wings, i.e. their positions, velocities and accelerations, were then calculated in sufficient detail to show how these quantities vary with time during one complete wing stroke. The aerodynamic lift and drag of the entire natural wing were measured in a wind tunnel with the wing arranged in different positions relative to the flow. By placing it in the boundary layer of the tunnel, the wind speed was graded from tip to base in approximately the same way as during the actual flight. There is therefore no error due to scale effect or to the induced drag. In most respects the wings resemble ordinary, slightly cambered airfoils. Their characteristics are given as polar diagrams. The kinematic and aerodynamic analyses make it possible to calculate the forces which act upon the locust at any instant of time. It is here necessary to presuppose that the non-stationary flight situations are essentially similar to a sequence of stationary situations. For locusts, this presupposition is justified: (i) from theoretical estimates of the quantitative effect of non-stationary flow; and (ii) from control measurements of the average thrust and lift produced during flight. It was found that the calculated vertical force, when averaged over an entire wing stroke, equalled the average reduction in body weight, as measured directly on the flight balance. Similarly, the average thrust of the wings corresponded to the drag of the body. The analysis shows how the aerodynamic forces vary during the wing stroke. The hindwings are responsible for about 70 % of the total lift and thrust. About 80 % of the lift is produced during the downstroke. During flight at normal lift the angles of attack (middle part of wing) are small during the upstroke and vary between 10 and 15° during the downstroke. When the lift was larger or smaller than the body weight these figures increased or decreased respectively. The forewings are peculiar in two ways: (i) during the middle part of the downstroke a true flap (the vannus) is put into action; (ii) during the upstroke the proximal part has a Z-shaped cross-section and gives but little lift and drag. The hindwings are characteristic in that the posterior part (vannus) is flexible and becomes moulded by the wind, increasing the angle of attack at which stalling occurs to about 25°. Since both the movements of the wings relative to the body and the aerodynamic forces are known at any instant, the exchange of power with the surrounding air can be calculated. The moments of inertia of the wing mass being known, the power for accelerating the wings can also be estimated. The sum of these contributions is the power which passes the wing fulcrum; this estimate is used in a later paper (part IX) where the energetics of flight is discussed in detail. The diagrams are correct to scale. The restriction of freedom caused by the suspension is discussed, together with the possible errors of a stationary analysis.

scholarly journals Manipulation of Miniature and Microminiature Bodies on a Harmonically Oscillating Platform by Controlling Dry Friction

Micromachines ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1087
Author(s):  
Sigitas Kilikevičius ◽  
Algimantas Fedaravičius ◽  
Virginija Daukantienė ◽  
Kristina Liutkauskienė ◽  
Linas Paukštaitis
Keyword(s):  
Dry Friction ◽  
The Body ◽  
Control Parameters ◽  
Friction Control ◽  
Vibrating Plates ◽  
Directional Motion ◽  
Novel Method ◽  
Nonprehensile Manipulation ◽  
Motion Characteristics ◽  
And Control

Currently used nonprehensile manipulation systems that are based on vibrational techniques employ temporal (vibrational) asymmetry, spatial asymmetry, or force asymmetry to provide and control a directional motion of a body. This paper presents a novel method of nonprehensile manipulation of miniature and microminiature bodies on a harmonically oscillating platform by creating a frictional asymmetry through dynamic dry friction control. To theoretically verify the feasibility of the method and to determine the control parameters that define the motion characteristics, a mathematical model was developed, and modeling was carried out. Experimental setups for miniature and microminiature bodies were developed for nonprehensile manipulation by dry friction control, and manipulation experiments were carried out to experimentally verify the feasibility of the proposed method and theoretical findings. By revealing how characteristic control parameters influence the direction and velocity, the modeling results theoretically verified the feasibility of the proposed method. The experimental investigation verified that the proposed method is technically feasible and can be applied in practice, as well as confirmed the theoretical findings that the velocity and direction of the body can be controlled by changing the parameters of the function for dynamic dry friction control. The presented research enriches the classical theories of manipulation methods on vibrating plates and platforms, as well as the presented results, are relevant for industries dealing with feeding, assembling, or manipulation of miniature and microminiature bodies.

scholarly journals TO THE THEORY OF n-DIMENSIONAL BRACHISTOCHRONE

2020 ◽  
pp. 53-60
Author(s):  
Gladkov S.O. ◽  
◽  
Bogdanova S.B. ◽  
Keyword(s):  
Three Dimensional ◽  
Plane Curve ◽  
Viscous Friction ◽  
Analytical Description ◽  
The Body ◽  
Viscous Drag ◽  
Friction Forces ◽  
Drag Forces ◽  
Moving Body ◽  
Plane Shape

In this paper, a solution to the problem of the motion of a brachistochrone in the ndimensional Euclidean space is firstly presented. The very first formulation of the problem in a two-dimensional case was proposed by J. Bernoulli in 1696. It represented an analytical description of the trajectory for the fastest rolling down under gravitational force only. Thereafter, a number of problems devoted to a brachistochrone were considered with account for gravitational forces, dry and viscous drag forces, and a possible variation in the mass of a moving body. Analytical solution to the formulated problem is presented in details by an example of the body moving along a brachistochrone in three-dimensional Cartesian coordinates. The obtained parametric solution is confirmed by a graphical interpretation of the calculated result. The formulated problem is solved for an ideal case when drag forces are neglected. If dry and viscous friction forces are taken into account, the plane shape of the brachistochrone remains the same,while the analysis of the solution becomes more complicated. When, for example, a side air flow is taken into account, the plane curve is replaced by a three-dimensional brachistochrone.

scholarly journals DISSIPATIVE OSCILLATORS’ POWER CHARACTERISTIC NON-SYMMETRY DYNAMIC EFFECT

2021 ◽  
pp. 65-75
Author(s):  
Vasiliy Olshanskiy ◽  
Stanislav Olshanskiy
Keyword(s):  
Differential Equation ◽  
Dry Friction ◽  
Elastic Characteristic ◽  
Approximation Error ◽  
Dynamic Effect ◽  
Viscous Friction ◽  
Equation Of Motion ◽  
Lambert Function ◽  
Coulomb Dry Friction ◽  
Non Linear Oscillator

The features of motion of a non-linear oscillator under the instantaneous force pulse loading are studied. The elastic characteristic of the oscillator is given by a polygonal chain consisting of two linear segments. The focus of the paper is on the influence of the dissipative forces on the possibility of occurrence of the elastic characteristic non-symmetry dynamic effect, studied previously without taking into account the influence of these forces. Four types of drag forces are considered, namely linear viscous friction, Coulomb dry friction, position friction, and quadratic viscous resistance. For the cases of linear viscous friction and Coulomb dry friction the analytical solutions of the differential equation of oscillations are found by the fitting method and the formulae for computing the swings are derived. The conditions on the parameters of the problem are determined for which the elastic characteristic non-symmetry dynamic effect occurs in the system. The conditions for the effect to occur in the system with the position friction are derived from the energy relations without solving the differential equation of motion. In the case of quadratic viscous friction the first integral of the differential equation of motion is given by the Lambert function of either positive or negative argument depending on the value of the initial velocity. The elastic characteristic non-symmetry dynamic effect is shown to occur for small initial velocities, whereas it is absent from the system when the initial velocities are sufficiently large. The values of the Lambert function are proposed to be computed by either linear interpolation of the known data or approximation of the Lambert function by elementary functions using asymptotic formulae which approximation error is less than 1%. The theoretical study presented in the paper is followed up by computational examples. The results of the computations by the formulae proposed in the paper are shown to be in perfect agreement with the results of numerical integration of the differential equation of motion of the oscillator using a computer.

STOCHASTIC VERSIONS OF ANOSOV'S AND NEISTADT'S THEOREMS ON AVERAGING

2001 ◽  
Vol 01 (01) ◽  
pp. 1-21 ◽  
Author(s):  
YURI KIFER
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hamiltonian Systems ◽  
Initial Conditions ◽  
Slow Motion ◽  
Averaging Principle ◽  
Integrable Hamiltonian Systems ◽  
Constant Energy ◽  
Slow Motions ◽  
Fast And Slow Motions

In systems which combine slow and fast motions the averaging principle says that a good approximation of the slow motion can be obtained by averaging its parameters in fast variables. This setup arises, for instance, in perturbations of Hamiltonian systems where motions on constant energy manifolds are fast and across them are slow. When these perturbations are deterministic Anosov's theorem says that the averaging principle works except for a small in measure set of initial conditions while Neistadt's theorem gives error estimates in the case of perturbations of integrable Hamiltonian systems. These results are extended here to the case of fast and slow motions given by stochastic differential equations.

An analysis of locomotor body movements in pronghorn antelope

1982 ◽  
Vol 60 (8) ◽  
pp. 1871-1880
Author(s):  
Robert E. Bullock
Keyword(s):  
Stride Length ◽  
Slow Motion ◽  
Vertical Movement ◽  
Center Of Gravity ◽  
The Body ◽  
Ground Contact ◽  
Body Movements ◽  
Pronghorn Antelope

Slow-motion film sequences of pronghorn antelope were analyzed to determine movements of the body and various body members during the most frequently employed gaits: walk, trot, canter (lope), and gallop. As speed and gait progress from a walk to a gallop, the angles at which the legs strike and leave the ground become more acute, the body is lower to the ground, and each leg moves through a greater arc during ground contact. Inasmuch as the body levels out somewhat, it is suggested that less energy may be required in raising the center of gravity. This may make more energy available for moving the legs. As speed increases, the feet are lifted progressively higher, the legs travel further, and the feet attain greater backward acceleration before striking the ground. In the gallop, the forelegs are kept fully extended until contacting the ground and the degree of spinal flexure is increased, thus extending stride length to its maximum. Vertical movement of the head increases in the faster gaits and appears to play a larger role in shifting the center of gravity, increasing speed, and maintaining equilibrium.

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