scholarly journals Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

2021 ◽  
Author(s):  
Yuriy Alyushin
Keyword(s):  
Kinetic Energy ◽  
Elastic Deformation ◽  
Elastic Energy ◽  
Forced Vibrations ◽  
The Body ◽  
Kinematic Parameters ◽  
Conservation Of Energy ◽  
Average Value ◽  
The Law ◽  
External Forces

The mechanisms of natural oscillations and resonance are described, considering the peculiarities of the transformation of elastic and kinetic energy in the implementation of the law of conservation of energy in local and integral volumes of the body, using the concept of mechanics based on the concepts of space, time and energy. When describing the motion in the Lagrange form, the elastic deformation energy of the particles is determined by the quadratic invariant of the tensor, whose components are the partial derivatives of Euler variables with respect to Lagrange variables. The increment of the invariant due to elastic deformation is represented as the sum of two scalars, one of which depends on the average value of the relative lengths of the edges of the particles in the form of an infinitesimal parallelepiped, the second is equal to the standard deviation of these lengths from the average value. It is shown that each of the scalars can be represented in the form of two dimensionless kinematic parameters of elastic energy, which participate in different ways in the implementation of the law of conservation of energy. One part of the elastic energy passes into kinetic energy and participates in the implementation of the law of conservation of energy for the body as a whole, considering external forces. The second part is not converted into kinetic energy but changes the deformed state of the particles in accordance with the equations of motion while maintaining the same level of the part of the elastic energy of the particles used for this. The kinematic parameters differ from the volume density of the corresponding types of energy by a factor equal to the elastic modulus, which is directly proportional to the density and heat capacity of the material and inversely proportional to the volume compression coefficient. Transverse, torsional, and longitudinal vibrations are considered free and under resonance conditions. The mechanisms of transformation of forced vibrations into their own after the termination of external influences and resonance at the superposition of free and forced vibrations with the same or similar frequency are considered. The formation of a new free wave at each cycle with an increase in the amplitude, which occurs mainly due to internal energy sources, and not external forces, is justified.

scholarly journals The abnormal kinetic energy of an ion in a gas

1913 ◽  
Vol 88 (603) ◽  
pp. 296-302 ◽  
Keyword(s):  
Kinetic Energy ◽  
Kinetic Theory ◽  
Negative Ions ◽  
Electric Force ◽  
Theoretical Support ◽  
Gas Molecule ◽  
Gas Molecules ◽  
The Law ◽  
External Forces ◽  
Equipartition Of Energy

1. In a paper on "The Charges on Ions in Gases, and the Effect of Water Vapour on the Motion of Negative Ions," Townsend showed that when a stream of ions is moving in an electric field the extent to which it spreads out as it advances depends on the dryness of the gas as well as on the electric force, indicating that the rate of diffusion in dry air is abnormally great in comparison with the velocity under an electric force. It was suggested ( loc. cit ., p. 469) that this could be explained on the supposition that the ions were not in "thermal equilibrium" with the molecules of the gas, but that their mean kinetic energy exceeded that of an equal number of gas molecules in the ratio k to unit), where k depends on the pressure and the electric force. Townsend mentioned a possible means by which this abnormal energy might arise, namely, that the extra velocity acquired by an ion in an interval between collisions was nod all lost by collision with a gas molecule, 80 that energy might accumulate for some time. The effect has been further studied by Haselfoot, both observers showing that k is, at any rate approximately, a function of X/ p only, where X is the electric forces and p the pressure of the gas. It seemed to the author that it would be desirable to investigate tbs matter quantitatively on the basis of the kinetic theory of gases, sines we are here dealing with the validity or non-validity oh the law of equipartition of energy. It is shown in this paper that it is easy enough to obtain theoretical support for the assumption of abnormal kinetic energy; in fact, the values of k predicted by pure theory are considerably in excess of those actually observed. In order to prevent misunderstanding, it may be stated that the law of equipartition of energy in the kinetic theory is only proved to be true when the molecules are left to themselves in tile absence of external forces.

scholarly journals Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 1133-1154
Author(s):  
Yury A. Alyushin
Keyword(s):  
Kinetic Energy ◽  
Elastic Energy ◽  
Superposition Principle ◽  
Forced Vibrations ◽  
Phase Changes ◽  
Initial State ◽  
Similar Frequency ◽  
Quadratic Invariant ◽  
Internal Sources ◽  
Lagrange Variables

The scientific novelty of this work is determined by the rationale for the participation in transformations, along with the kinetic energy of particles, of four types of elastic energy, identified by the peculiarities of their phase changes in the oscillation process. Two types are converted into kinetic energy, while the other two types change the deformed state of particles in accordance with the equations of motion due to internal sources. The result is obtained based on the use of the superposition principle in the space of Lagrange variables with the imposition of forced and free oscillations, as well as a new model of mechanics based on the concepts of space, time, and energy with a new scale of average stresses that takes into account the energy of particles in the initial state. In such a model of mechanics, a generalized measure of the elastic energy of particles is a quadratic invariant of asymmetric tensor whose components are partial derivatives of Euler variables with respect to Lagrange variables. The concept of kinematic energy parameters is introduced, which differ from the corresponding volumetric energy densities by a multiplier equal to the modulus of elasticity, which is directly proportional to the density and heat capacity of the material, and inversely proportional to the volumetric compression coefficient. Comparison of the values of kinematic parameters shows that most of the energy required for oscillations is associated with the deformation of particles and comes from internal sources. The mechanisms of transformation of forced vibrations into their own for transverse, torsional, and longitudinal vibrations are considered, as well as the occurrence of resonance when free and forced vibrations are superimposed with the same or a similar frequency. The formation of a new free wave after each cycle of external influences with an increase in amplitude, which occurs mainly due to internal, and not external, energy sources is justified.

scholarly journals Forensic Analysis Of Low Speed Vehicle Collisions

2003 ◽  
Vol 20 (1) ◽  
Author(s):  
John A. DOnofrio
Keyword(s):  
Kinetic Energy ◽  
Forensic Analysis ◽  
The Body ◽  
Conservation Of Energy ◽  
Low Speed ◽  
Stop Sign ◽  
Post Impact ◽  
Energy Dissipated ◽  
Energy Absorbing ◽  
Crash Tests

A Low Speed Collision Is Defined, For The Purpose Of This Paper, As A Collision Between Two Vehicles That Produces No Permanent Damage To The Body Of The Vehicle Except To The Bumper System. The Vehicles Are Equipped With Energy Absorbing Bumpers That Are Rated To A Particular Speed. The Collisions Are, For All Intents And Purposes, In-Line In Nature (Collinear) And Without Post-Impact Rotation. This Definition, While Quite Specific, Covers A Large Number Of Collisions. They Are The Typical Stop Sign, Waiting In Traffic, Parking Lot Type Crash. In The Following Sections I Will Examine How These Vehicles Interact And Respond To Such Collisions By Applying Newtons Laws And The Data From Vehicle Crash Tests. Presented Is Methodology For Reconstructing The Pre-Impact And Post-Impact Speed Of Such Collisions Using The Following Protocol: 1. Compute The Kinetic Energy Dissipated In The Collision From The Characteristics Of The Vehicles And Their Bumpers As Revealed In Crash Tests. 2. Use Conservation Of Energy And Damage Relationships To Determine The Pre-Collision Kinetic Energy And Closing Speed Of The Two-Vehicle System. 3. Use Conservation Of Linear Momentum To Calculate The Post-Collision Speed And Delta-V Of The Two Vehicles. This Method Uses The Strict Application Of Newtons Laws And Treats Both Vehicles As A System.

scholarly journals The loss of energy of an α- ray beam in its passage through matter. Part I. — Passage through air and CO 2

1922 ◽  
Vol 102 (714) ◽  
pp. 48-71 ◽  
Keyword(s):  
Kinetic Energy ◽  
Equivalent Amount ◽  
Conservation Of Energy ◽  
Surrounding Space ◽  
The Law

An α -particle, emitted from a radio-active body, will, during its passage through matter, gradually lose kinetic energy. The experiments of Rutherford and Robinson have shown that this kinetic energy is converted into an equivalent amount of heat generated in the matter. These experiments confirm the law of the conservation of energy, but give no indication of the mechanism whereby the energy is given to the surrounding space. This mechanism has been examined theoretically by Thomson, Bohr, and Darwin, who proved that the energy of the α -ray, when passing near an atom, was first given to the electrons, which, in turn, yielded their energy to the atom. The manner in which the α -particle yields its energy to the electrons depends, on the average, on the speed of the α -particle, and on the number and arrangement of the electrons within the atom.

Numerical Analysis of the Workpiece Velocity in Electromagnetic Forming Process

2011 ◽  
Vol 314-316 ◽  
pp. 634-638
Author(s):  
Li Qiu ◽  
Yi Liang Lv ◽  
Cheng Xi Jiang ◽  
Xiao Tao Han ◽  
Liang Li
Keyword(s):  
Numerical Analysis ◽  
Kinetic Energy ◽  
Differential Equations ◽  
Electromagnetic Force ◽  
Electrical Energy ◽  
Electromagnetic Forming ◽  
Forming Process ◽  
Conservation Of Energy ◽  
The Law

The effect of the motional electromagnetic force in the electromagnetic forming circuit on the workpiece velocity is analyzed. The differential equations of unconsidering and considering the motional electromagnetic force in the electromagnetic forming circuit are solved numerically. The results without considering the motional electromagnetic force are unavailable because they violate the law of conservation of energy, while the results with considering the motional electromagnetic force can accurately reflect the electromagnetic forming process. Furthermore, it is found that the electrical energy transforms into the kinetic energy due to the motional electromagnetic force.

CHARACTERISTICS OF FREE-RADICAL PROCESSES IN THE ORGANISMS OF SOME PREDATORY FISH SPECIES IN DIFFERENT SEASONS OF THE YEAR

2017 ◽  
pp. 117-123
Author(s):  
Nikolay Aleksandrovich Pudovkin ◽  
Peter Vladimirovich Smutnev
Keyword(s):  
Fish Species ◽  
Catalase Activity ◽  
Perca Fluviatilis ◽  
Selenium Concentration ◽  
The Body ◽  
Predatory Fish ◽  
Volga River ◽  
Silurus Glanis ◽  
Average Value ◽  
Pike Perch

The authors of the article have studied the content of the elements of anti-oxidant system (malondialdehyde, catalase, selenium) in tissues of the internal organs (gills, intestine, muscles, liver, swimbladder, scales) in some species of predatory fish (pike Esox lucius (L., 1758), perch Perca fluviatilis (L., 1758), pike-perch Sander lucioperca (L., 1758), catfish Silurus glanis ) widespread in the basin of the Volga river in the Saratov region. The lowest concentration of malondialdehyde in organisms of the studied fish species is observed in fall and winter; the highest - in spring and summer. Catalase activity in gills tissue of a pike raised in 11.8%, cat-fish - 9.1%, pike-perch - 7.5%, perch - 7.8%. In fall (compared to winter) enzyme activity lowering in gonads of pike-perch makes 16.3%, in gonads of perch - 14.4%. In other tissues there were not observed any evident changes of catalase activity. Fish species under consideration are listed according to the average value of selenium concentration in organisms, µg/g: pike (0.208) > catfish (0.207) > pike-perch (0.196) > perch (0.178). According to the average value of the selenium accumulation in the body in different season all the studied species can be placed in the following order, µg/g: winter-pike (0.132) > pike-perch (0.136) > perch and catfish (0.142); spring - pike-perch (0.190) > perch (0.191) > pike (0.208) > catfish (0.209); summer - perch (0.186) > pike-perch (0.190) > catfish and pike (0.203); autumn - perch (0.193) > pike-perch (0.268) > > catfish (0.274) > pike (0.289).

The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

1950 ◽  
Vol 1 (4) ◽  
pp. 305-318
Author(s):  
G. N. Ward
Keyword(s):  
Supersonic Flow ◽  
Velocity Potential ◽  
Operational Calculus ◽  
The Body ◽  
Body Of Revolution ◽  
Internal Flows ◽  
Flow Past ◽  
External Forces ◽  
Internal Pressures ◽  
Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

Weight-loss diets and the law of conservation of energy

1981 ◽  
Vol 58 (12) ◽  
pp. 996
Author(s):  
John W. Hill
Keyword(s):  
Weight Loss ◽  
Conservation Of Energy ◽  
The Law

Moving Cage: Vibration, Sonification and the Quanta of Time

2021 ◽  
Vol 46 (2) ◽  
pp. 169-183
Author(s):  
MARCUS CHENG CHYE TAN
Keyword(s):  
Kinetic Energy ◽  
The Body ◽  
Dance Movements ◽  
Politics Of The Body

Dear John is an experimental choreomusical work that reinterprets Cage's works while advancing his ideas of sound as sonic events and embodied choreography. In this episodic work, improvised movement unfolds to a soundscape of defamiliarized instruments, sound devices and sonicities of macro- and micro-movements. The correspondence and (in)congruence between dance movements and music's kinetic energy become the means to examine a politics of the body and sound, of music on movement. Additionally, in this ‘auditory architecture’ the quanta of time, its relations and (lack of) unity are exposed. This article then examines the intersubjective interplay of movement and music, body and sonicity; it considers the resonance of the performing body as intermaterial vibration and how this invites a sonic politics of relational possibility. The article will then also investigate the ways in which the interaction of motion and music, movement and stillness engenders experiences of time's indeterminacy and elasticity.

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