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 Correction of the Koenig Formula for the Kinetic Energy of a Rotating Solid

2021 ◽  
Author(s):  
Yuriy Alyushin
Keyword(s):  
Kinetic Energy ◽  
Superposition Principle ◽  
The Body ◽  
Initial State ◽  
Moments Of Inertia ◽  
Lagrange Form ◽  
Joint Plane ◽  
Angular Velocities ◽  
The Difference ◽  
Cyclic Changes

An exact solution is obtained for the kinetic energy in the general case of the spatial motion of solids with arbitrary rotation, which differs from the Koenig formula by three additional terms with centrifugal moments of inertia. The description of motion in the Lagrange form and the superposition principle are used, which provides a geometric summation of the velocities and accelerations of the joint motions in the Lagrange form for any particle at any time. The integrand function in the equation for kinetic energy is represented by the sum of the identical velocity components of the joint plane-parallel motions. The moments of inertia in the Koenig formula do not change during movement and can be calculated from the current or initial state of the body. The centrifugal moments change and turn to 0 when rotating relative to the main central axes only for bodies with equal main moments of inertia, for example, for a ball. In other cases, the difference in the main moments of inertia leads to cyclic changes in the kinetic energy with the possible manifestation of precession and nutation, the amplitude of which depends on the angular velocities of rotation of the body. An example of using equations for a robot with one helical and two rotational kinematic pairs is given.

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 Experimental and numerical studies of an eastward jet over topography

2001 ◽  
Vol 438 ◽  
pp. 129-157 ◽  
Author(s):  
YUDONG TIAN ◽  
ERIC R. WEEKS ◽  
KAYO IDE ◽  
J. S. URBACH ◽  
CHARLES N. BAROUD ◽  
...  
Keyword(s):  
Parameter Space ◽  
Laboratory Experiments ◽  
Multiple Equilibria ◽  
Low Frequency ◽  
Zonal Flow ◽  
Azimuthal Velocity ◽  
Flow Patterns ◽  
Initial State ◽  
Similar Frequency ◽  
Zonal Flows

Motivated by the phenomena of blocked and zonal flows in Earth's atmosphere, we conducted laboratory experiments and numerical simulations to study the dynamics of an eastward jet flowing over wavenumber-two topography. The laboratory experiments studied the dynamical behaviour of the flow in a barotropic rotating annulus as a function of the experimental Rossby and Ekman numbers. Two distinct flow patterns, resembling blocked and zonal flows in the atmosphere, were observed to persist for long time intervals.Earlier model studies had suggested that the atmosphere's normally upstream- propagating Rossby waves can resonantly lock to the underlying topography, and that this topographic resonance separates zonal from blocked flows. In the annulus, the zonal flows did indeed have super-resonant mean zonal velocities, while the blocked flows appear subresonant. Low-frequency variability, periodic or irregular, was present in the measured time series of azimuthal velocity in the blocked regime, with dominant periodicities in the range of 6–25 annulus rotations. Oscillations have also been detected in zonal states, with smaller amplitude and similar frequency. In addition, over a large region of parameter space the two flow states exhibited spontaneous, intermittent transitions from the one to the other.We numerically simulated the laboratory flow geometry in a quasi-geostrophic barotropic model over a similar range of parameters. Both flow regimes, blocked and zonal, were reproduced in the simulations, with similar spatial and temporal characteristics, including the low-frequency oscillations associated with the blocked flow. The blocked and zonal flow patterns are present over wide ranges of forcing, topographic height, and bottom friction. For a significant portion of parameter space, both model flows are stable. Depending on the initial state, either the blocked or the zonal flow is obtained and persists indefinitely, showing the existence of multiple equilibria.

scholarly journals INSTRUMEN TES ISLAM KIMIA (ITIK) UNTUK MENDETEKSI PEMAHAMAN LEVEL MIKROSKOPIS MATERI AIR

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Asih Widi Wisudawati
Keyword(s):  
High School ◽  
Hydrogen Bonding ◽  
Kinetic Energy ◽  
Research And Development ◽  
Atomic Mass ◽  
Microscopic Level ◽  
Phase Changes ◽  
Relative Atomic Mass ◽  
Level Of Understanding ◽  
Particle Kinetic Energy

The study aims to develop instrument to measurethe level of understanding of students and microscopic level material phase changes of water. The method used is R&D (Research and Development) Borg and Gall, which have procedure were are following step (1) Need assessment/ Plan (2) Design product/ Organization (3) Created product/ implementation. Implementation with one shot design study with samples used a number of 71 students of 10th grade MA Wahid Hasyim and senior high school MBS Yogyakarta. Indicators in the study is the movement and vibration of water particles, the distance between water particles, particle kinetic energy of water, relative atomic mass of water and hydrogen bonding. The results showed an understanding of chemica lmaterial microscopic level is low and spitual attitude as a nurturant effect is high categories. 

scholarly journals Adjoint Sensitivity of North Pacific Atmospheric River Forecasts

2019 ◽  
Vol 147 (6) ◽  
pp. 1871-1897 ◽  
Author(s):  
Carolyn A. Reynolds ◽  
James D. Doyle ◽  
F. Martin Ralph ◽  
Reuben Demirdjian
Keyword(s):  
Kinetic Energy ◽  
Forecast Error ◽  
Meridional Wind ◽  
Precipitation Forecast ◽  
Initial State ◽  
Adjoint Sensitivity ◽  
Optimal Perturbation ◽  
Low Level ◽  
Atmospheric River ◽  
Perturbation Growth

Abstract The initial-state sensitivity and optimal perturbation growth for 24- and 36-h forecasts of low-level kinetic energy and precipitation over California during a series of atmospheric river (AR) events that took place in early 2017 are explored using adjoint-based tools from the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS). This time period was part of the record-breaking winter of 2016–17 in which several high-impact ARs made landfall in California. The adjoint sensitivity indicates that both low-level winds and precipitation are most sensitive to mid- to lower-tropospheric perturbations in the initial state in and near the ARs. A case study indicates that the optimal moist perturbations occur most typically along the subsaturated edges of the ARs, in a warm conveyor belt region. The sensitivity to moisture is largest, followed by temperature and winds. A 1 g kg−1 perturbation to moisture may elicit twice as large a response in kinetic energy and precipitation as a 1 m s−1 perturbation to the zonal or meridional wind. In an average sense, the sensitivity and related optimal perturbations are very similar for the kinetic energy and precipitation response functions. However, on a case-by-case basis, differences in the sensitivity magnitude and optimal perturbation structures result in substantially different forecast perturbations, suggesting that optimal adaptive observing strategies should be metric dependent. While the nonlinear evolved perturbations are usually smaller (by about 20%, on average) than the expected linear perturbations, the optimal perturbations are still capable of producing rapid nonlinear perturbation growth. The positive correlation between sensitivity magnitude and wind speed forecast error or precipitation forecast differences supports the relevance of adjoint-based calculations for predictability studies.

The Lanchester Damper—A Design Procedure for Optimizing the Damping Ratio for a Cylindrical Slug Damper Fitted to a Machine Element

1979 ◽  
Vol 101 (2) ◽  
pp. 291-297 ◽  
Author(s):  
Y. H. J. Au ◽  
K. W. Ng ◽  
R. W. New
Keyword(s):  
Kinetic Energy ◽  
Optimum Condition ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Design Procedure ◽  
Forced Vibrations ◽  
Parent Body ◽  
Standard Theory ◽  
Machine Element

The present work shows how the equations of motion for a Lanchester damper can be modified to include the effects of a damper slug rolling inside a cavity within the parent body, and of the kinetic energy of the damping fluid. The effect of the slug rolling is to reduce the performance of the damper below that predicted by the standard theory and to require a different value for damping at the optimum condition. These effects are significant when the build-up of self-excited type of vibrations are to be prevented, and when small forced vibrations are to be controlled. Fluid kinetic energy effects can be neglected when the damping fluid is gaseous, but not necessarily so when it is a liquid.

Energy considerations in the instability of a current-vortex sheet

1961 ◽  
Vol 57 (3) ◽  
pp. 628-637 ◽  
Author(s):  
D. H. Michael
Keyword(s):  
Kinetic Energy ◽  
Magnetic Energy ◽  
Fluid Motion ◽  
Dissipative System ◽  
Vortex Sheet ◽  
Point Of View ◽  
Initial State ◽  
Linearized Stability ◽  
The Mean ◽  
A Current

In the normal procedure for establishing linearized stability criteria a mean steady state which we denote by U is perturbed by a small additional disturbance u in the Eulerian sense. In the linearization it is usual to regard the disturbance as resolved into Fourier components which are additive so far as the first order goes. The linearized problem will then determine a time amplification factor eiσr so that the linearized disturbance is of the form uexp{i(αx + σt)} and the whole motion U + uexp{i(αx + σt)}. As usual it is implied that the real part of complex functions such as uexp{i(αx + σt)} be taken. In cases of instability (imaginary part of σ negative), where the magnitude of the disturbance increases with the time, we are prompted to ask how energy is supplied to the disturbance. This question is especially relevant to many of the classical problems of fluid motion instability in which the systems are self-contained in the sense that energy is neither supplied nor withdrawn by an outside agency. If such a system is non-dissipative we expect that the total energy of the organized motion and the electromagnetic field, if present, shall be conserved, whilst such energy in a dissipative system will be gradually reduced by heat losses. In either case energy which is taken into a growing disturbance must be provided from the mean energy stored in the system in its initial state. One of the simplest cases of instability to examine from this point of view is the Helmholtz instability of a plane in viscid vortex sheet. This system is self-contained and conservative in the energy of the organized motion, and moreover the only form of energy with which we have to deal is kinetic energy. In the first part of this note we examine how disturbance kinetic energy is provided in this case by the break up of the organized motion of the mean stream. In the second part we consider what happens to the energy balance of a current-vortex sheet in the non-dissipative case. There are here two forms of energy, kinetic and magnetic, and it is shown that when the interface is unstable the overall magnetic energy increases at the expense of the kinetic energy.

The reversal of chemical reactions in contracting muscle during an applied stretch

1959 ◽  
Vol 151 (943) ◽  
pp. 169-193 ◽  
Keyword(s):  
Elastic Energy ◽  
Active Phase ◽  
Total Heat ◽  
Net Energy ◽  
Initial State ◽  
Contracting Muscle ◽  
A Value ◽  
Complete Reversal ◽  
Sudden Release ◽  
Chemical Products

When a toad muscle is stretched 11 to 20 % during the active phase of a twitch or a short tetanus, resisting strongly, the total heat ( H s ) appearing in it up to the end of relaxation may be about equal to the total mechanical work ( W 0 ) done during the stretch. Since all the work has disappeared, and no elastic energy is left by the end of relaxation, the net energy ( H s – W 0 ) liberated by the muscle itself is nil. It is concluded that the chemical products of the reaction provoked by the stimulus have been wholly returned to their initial state. This result depends on the amplitude and timing of the stretch. Often H s is rather greater than W 0 , but ( H s – W 0 ) is always much less than H i , the total heat in an isometric contraction: in these circumstances most, but not all, of the chemical products of activity have been reinstated. During a contraction with stretch the contractile component begins to lengthen as soon as the tension reaches a value slightly greater than that in an isometric tetanus. It is during this lengthening that chemical energy is re-absorbed. When work W , up to any moment, is done on a contracting muscle, some of it is used in producing elastic energy E in the series elastic component and in the connexion to the ergometer. Only the net work W n =( W – E ) has been taken up by the contractile component. If H is the heat produced in the muscle by any moment ( H – W n ) soon begins to fall when the stretch starts. In a twitch or a short tetanus ( H – W n )usually becomes substantially negative, remaining negative for a considerable period but finally returning to zero, or to a small positive value, by the end of relaxation. In a longer tetanus, with a stretch starting later and the stimulus outlasting it, ( H – W n )begins to fall directly the stretch starts, dropping sometimes to or below zero, but increasing rapidly when the stretch ends, as the stimulus continues. The fact that the net energy ( H — W n ) liberated by a muscle up to any moment may reach large negative values during part of the cycle, while the total energy ( H s — W 0 ) over the whole cycle never falls below zero, is difficult to explain on any simple theory of the reversal of a chemical reaction. The difficulty is resolved by assuming that whenever the tension rises by ∆ P during contraction, for whatever cause, there is a corresponding ‘thermoelastic’ absorptionof heat ∆ Q = 0.018 l 0 ∆ P , and conversely when the tension falls. The constant 0.018 is that observed in earlier experiments on the thermal effect of a sudden release of tension. If this assumption is correct, the real heat produced by the muscle up to any moment is greater than H by Q = 0.018 l 0 P , where P is the tension at that moment. Substituting ( H + Q ) for H , it is found that ( H + Q — W n ) behaves in the same general way as ( H — W n ) during and after a stretch but never becomes negative. Since Q is zero at the end of relaxation, when P = 0, the statement about total quantities stands unaltered. The results can be used to calculate the ratio of the energy absorbed in chemical resynthesis, during a stretch, to the work applied. In stretches of moderate extent, the ratio may be as high as 0.5, but in the longer and more vigorous stretches which gave complete reversal the ratio was considerably less. The thermodynamic implications are discussed.

Influence of temperature on structural-phase changes and physical properties of ceramics on the basis of aluminum oxide and silicon

2020 ◽  
Vol 62 (7) ◽  
pp. 716-720
Author(s):  
N. Kantay ◽  
N. Kasmamytov ◽  
B. Rakhadilov ◽  
S. Plotnikov ◽  
M. Paszkowski ◽  
...  
Keyword(s):  
Monoclinic Phase ◽  
Raw Materials ◽  
Structural Phase ◽  
Phase Changes ◽  
Initial State ◽  
Influence Of Temperature ◽  
X Ray ◽  
Influence Of Temperature On ◽  
Scanning Electron ◽  
High Voltage Porcelain

Abstract The purpose of this experiment was to prepare high-voltage porcelain ceramics as local raw materials. Density, water absorption, and volume shrinkage were determined according to the State standard (GOST 7025-91). A structural analysis was carried out using a scanning electron microscope, and an X-ray phase analysis was carried out on an Xpert PRO diffractometer. It was found, that in the initial state, ceramics consist of hexagonal (SiO2) and a small amount of monoclinic phase. Above a temperature of 1150 °С they consist of hexagonal (SiO2), an orthorhombic lattice, and also contain mullite (Al2Si2O13).

Calculation of anisotropic photoionization cross sections. I. Hydrogen atom

1968 ◽  
Vol 46 (24) ◽  
pp. 2719-2731 ◽  
Author(s):  
Sheng Hsien Lin
Keyword(s):  
Angular Distribution ◽  
Hydrogen Atom ◽  
Kinetic Energy ◽  
Cross Sections ◽  
Bound State ◽  
Atomic Unit ◽  
Initial State ◽  
Total Cross Sections

The differential and total cross sections of photoionization of the hydrogen atom from the states 1s, 2s, 2pm, 3pm, 3dm, and 4dm are calculated for the photoelectron kinetic energy E from E = 0.01 atomic unit to E = 2.00 atomic unit. It is found that when the magnetic sublevels of the initial state are equally populated, the angular distribution of photoelectrons has the behavior[Formula: see text]and, besides 1s and 2s states, the angular distribution of photoelectrons from np state, nd state, etc. will become isotropic at a particular photoelectron kinetic energy. The angular distribution of photoelectrons for the case in which the magnetic sublevels of the initial bound state are unequally populated is also discussed.

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