scholarly journals Study of a Stripper Header for Grain Harvesting as a Vibrating System

2021 ◽  
Vol 31 (3) ◽  
pp. 403-413
Author(s):  
Vladimir Yu. Savin
Keyword(s):  
Differential Equation ◽  
Mathematical Description ◽  
Elastic Element ◽  
Lagrange Equation ◽  
Oscillatory System ◽  
Angular Frequency ◽  
Forced Oscillations ◽  
Disturbing Force ◽  
Vibration Effect ◽  
Generalized Force

Introduction. Grain losses caused by stripping defects are the main problem to be solved in designing a stripper header. To reduce these losses, a design of a stripper header with a vibration drive is proposed. This device combines the processes of stripping grain crops and the vibration effect of the stripping fingers upon the ears of plants. The most important stage of the mathematical description of these processes is composing the differential equation of the stripping fingers motion. Materials and Methods. A computational-graphic diagram of an oscillatory system with one degree of freedom is proposed. To compose the differential equation of the stripping fingers motion, a method based on the application of the Lagrange equation was used. The oscillations of the system under studying arise from the motion of a point in the system according to a given law. The problem of kinematic excitation is reduced to the problem of force perturbation. This stage of the study was carried out without taking into account the resistance forces. Results. An equation for motion of stripping fingers making vibrational reciprocating movements is obtained. It is proposed to select the elastic element in the design scheme and consider a more general case of the stripping fingers movement. In this case, the movement of the stripping fingers is considered to be difficult. A characteristic feature of the mathematical description is the presence of a generalized force of potential forces. The differential equation of motion of a comb in the presence of an elastic element and the solution of this equation are composed. Discussion and Conclusion. Forced oscillations of a system without resistance, excited by a harmonic disturbing force, are harmonic oscillations with constant amplitude. On close values of the angular frequency of vibration of the drive output link and the root of the ratio of the stiffness coefficient of the elastic element to the stripping fingers mass, the case of resonance takes place. The system parameters must be selected so as to avoid this negative phenomenon.

scholarly journals THE BASIS OF THE EFFECTS OF MECHANICAL EXPLOSIVES ON THE PROCESS OF MASS SUGAR PROCESSING

2019 ◽  
pp. 68-74
Author(s):  
Oleg Omelyanov
Keyword(s):  
Mathematical Description ◽  
Raw Materials ◽  
Forced Oscillations ◽  
Mechanical Vibrations ◽  
Vibration Machine ◽  
Disturbing Force ◽  
Technological Processes

The article presents a mathematical description of the process of vibration processing of bulk raw materials. The vibration machine is considered as a system that performs forced oscillations under the action of a disturbing force that does not depend on the oscillations of the operating body. On the basis of the results of the study of the influence of mechanical vibrations on the process of separation of bulk products, an attempt is made to outline an approach to solving the problems of the theory of the influence of mechanical vibrations on technological processes.

Mechanical impedances of lungs and chest wall in the cat

1992 ◽  
Vol 73 (2) ◽  
pp. 427-433 ◽  
Author(s):  
Z. Hantos ◽  
A. Adamicza ◽  
E. Govaerts ◽  
B. Daroczy
Keyword(s):  
Chest Wall ◽  
Respiratory System ◽  
Small Volume ◽  
Angular Frequency ◽  
Forced Oscillations ◽  
Amplitude Dependence ◽  
Volume Changes ◽  
The Real ◽  
Output Flow ◽  
Frequency Independent

In nine anesthetized and paralyzed cats, the mechanical impedances of the total respiratory system (Zrs) and the lungs (ZL) were measured with small-volume pseudorandom forced oscillations between 0.2 and 20 Hz. ZL was measured after thoracotomy, and chest wall impedance (Zw) was calculated as Zw = Zrs-ZL. All impedances were determined by using input airflow [input impedance (Zi)] and output flow measured with a body box [transfer impedance (Zt)]. The differences between Zi and Zt were small for Zrs and negligible for ZL. At 0.2 Hz, the real and imaginary parts of ZL amounted to 33 +/- 4 and 35 +/- 3% (SD), respectively, of Zrs. Up to 8 Hz, all impedances were consistent with a model containing a frequency-independent resistance and inertance and a constant-phase tissue part (G-jH)/omega alpha, where G and H are coefficients for damping and elastance, respectively, omega is angular frequency, and alpha determines the frequency dependence of the real and imaginary parts. G/H was higher for Zw than for ZL (0.29 +/- 0.05 vs. 0.22 +/- 0.04, P less than 0.01). In four cats, the amplitude dependence of impedances was studied: between oscillation volumes of 0.8 and 3 ml, GL, HL, Gw, and Hw decreased on average by 3, 9, 26, and 29%, respectively, whereas the change in G/H was small for both ZL (7%) and Zw (-4%). The values of H were two to three times higher than the quasistatic elastances estimated with greater volume changes (greater than 20 ml).

scholarly journals ON OSCILLATIONS DESCRIBING A GENERALIZED DIFFERENTIAL RELAY EQUATION

2020 ◽  
pp. 53-60
Author(s):  
Vasiliy Olshansky ◽  
Stanislav Olshansky ◽  
Oleksіі Tokarchuk
Keyword(s):  
Differential Equation ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Equation Of Motion ◽  
Resistance Force ◽  
Oscillatory Process ◽  
Initial Deviation ◽  
Approximate Analytical Solutions ◽  
Positive Exponent ◽  
Generalized Differential

The motion of an oscillatory system with one degree of freedom, described by the generalized Rayleigh differential equation, is considered. The generalization is achieved by replacing the cubic term, which expresses the dissipative strength of the equation of motion, by a power term with an arbitrary positive exponent. To study the oscillatory process involved the method of energy balance. Using it, an approximate differential equation of the envelope of the graph of the oscillatory process is compiled and its analytical solution is constructed from which it follows that quasilinear frictional self-oscillations are possible only when the exponent is greater than unity. The value of the amplitude of the self-oscillations in the steady state also depends on the value of the indicator. A compact formula for calculating this amplitude is derived. In the general case, the calculation involves the use of a gamma function table. In the case when the exponent is three, the amplitude turned out to be the same as in the asymptotic solution of the Rayleigh equation that Stoker constructed. The amplitude is independent of the initial conditions. Self-oscillations are impossible if the exponent is less than or equal to unity, since depending on the initial deviation of the system, oscillations either sway (instability of the movement is manifested) or the range decreases to zero with a limited number of cycles, which is usually observed with free oscillations of the oscillator with dry friction. These properties of the oscillatory system are also confirmed by numerical computer integration of the differential equation of motion for specific initial data. In the Maple environment, the oscillator trajectories are constructed for various values of the nonlinearity index in the expression of the viscous resistance force and a corresponding comparative analysis is carried out, which confirms the adequacy of approximate analytical solutions.

scholarly journals Theoretical Vibration Analysis Regarding Excitation due to Elliptical Shaft Journals in Sleeve Bearings of Electrical Motors

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Ulrich Werner
Keyword(s):  
Differential Equation ◽  
Mathematical Description ◽  
Vibration Analysis ◽  
Equation System ◽  
Electrical Machines ◽  
Differential Equation System ◽  
Kinematic Constraints ◽  
Linear Differential ◽  
Electrical Motors ◽  
Rotor Mass

This paper shows a theoretical vibration analysis regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors, based on a simplified rotordynamic model. It is shown that elliptical shaft journals lead to kinematic constraints regarding the movement of the shaft journals on the oil film of the sleeve bearings and therefore to an excitation of the rotordynamic system. The solution of the linear differential equation system leads to the mathematical description of the movement of the rotor mass, the shaft journals, and the sleeve bearing housings. Additionally the relative movements between the shaft journals and the bearing housings are deduced, as well as the bearing housing vibration velocities. The presented simplified rotordynamic model can also be applied to rotating machines, other than electrical machines. In this case, only the electromagnetic spring valuecmhas to be put to zero.

Analysis of a Nonlinear Dynamic Vibration Absorber

1953 ◽  
Vol 20 (4) ◽  
pp. 515-518
Author(s):  
L. A. Pipes
Keyword(s):  
Forced Oscillations ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Nonlinear Characteristics ◽  
Disturbing Force ◽  
Main Mass ◽  
Dynamic Vibration ◽  
Nonlinear Force ◽  
Linear Spring ◽  
Force Displacement

Abstract This paper presents a mathematical analysis of the action of a dynamic vibration absorber. The system analyzed consists of a main mass attached to a rigid foundation by a linear spring coupled to the absorber mass by a spring of nonlinear characteristics. The forced oscillations of the system produced by a harmonic disturbing force acting on the main mass are studied analytically. It is assumed that the coupling absorber spring has nonlinear force-displacement characteristics of the hyperbolic sine type. Expressions for the amplitudes of the vibrations of the two masses as functions of the frequency of the disturbing force are obtained.

Stability Analysis of Inhaul Cable on Cable-Stayed Awning with Steel Structure Considering the Wind-Rain-Induced Vibration Effect

2013 ◽  
Vol 661 ◽  
pp. 112-115
Author(s):  
Xiao Zhao ◽  
Qing Yuan Wang ◽  
Yong Jie Liu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Vibration Analysis ◽  
Dynamic Theory ◽  
Steel Structure ◽  
Small Mass ◽  
Structural Dynamic ◽  
Vibration Effect ◽  
Set Up ◽  
Main Factor

Due to the applicable installation overhang large span, small mass, flexible characteristic, and small damp, the cable-stayed steel structure awning (CSSSA) could easily result in vibration with the wind load. The main factor is the turbulence wind and wind-rain induced vibration. Combining the structural dynamic theory, and considering the characteristic of the CSSSA, a motion differential equation is set up considering the wind-rain induced vibration, analysis cable-stayed stability under wind-rain induced vibration effect, and compare with the existing engineering result. Hope to provide some reference for similar designs.

Hydromechanics of lunate-tail swimming propulsion. Part 2

1977 ◽  
Vol 79 (1) ◽  
pp. 49-69 ◽  
Author(s):  
M. G. Chopra ◽  
T. Kambe
Keyword(s):  
Swimming Performance ◽  
Leading Edge ◽  
Angular Frequency ◽  
Optimum Shape ◽  
Physical Parameters ◽  
Sweep Angle ◽  
Propulsive Efficiency ◽  
Generalized Force ◽  
Total Thrust ◽  
The Mean

This paper investigates the propulsive performance of the lunate tails of aquatic animals achieving high propulsive efficiency (the hydromechanical efficiency being defined as the ratio of the work done by the mean forward thrust to the mean rate at which work is done by the tail movements on the surrounding fluid). Small amplitude heaving and pitching motions of a finite flat-plate wing of general planform with a rounded leading edge and a sharp trailing edge are considered. This is a generalization of Chopra's (1974) work on model rectangular tails. This motion characterizes vertical oscillations of the horizontal tail flukes of some cetacean mammals. The same oscillations, turned through a right angle to become horizontal motions of side-slip and yaw, characterize the caudal fins of certain fast-swimming fishes; viz. wahoo, tunny, wavyback skipjack, etc., from the Percomorphi and whale shark, porbeagle, etc., from the Selachii. Davies’ (1963, 1976) method of finding the loading distribution on the wing and generalized force coefficients, through approximate solution of an integral equation relating the loading and the upwash (lifting-surface theory), is used to find the total thrust and the rate of working of the tail, which in turn specify the hydromechanical swimming performance of the animals. The physical parameters concerned are the tail aspect ratio ((span)2/planform area), the reduced frequency (angular frequency x typical length/forward speed), the feathering parameter (the ratio of the tail slope to the slope of the path of the pitching axis), the position of the pitching axis, and the curved shapes of the leading and trailing edges. The variation of the thrust and the propulsive efficiency with these parameters has been discussed to indicate the optimum shape of the tail. It is found that, compared with a rectangular tail, a curved leading edge as in lunate tails gives a reduced thrust contribution from the leading-edge suction for the same total thrust; however, a sweep angle of the leading edge exceeding about 30° leads to a marked reduction of efficiency. Another implication of the present analysis is that no negative work is involved in the actual oscillation of the tail.The present results are used to obtain an estimate of the drag coefficient for the motion of the animals, based on observed data and the computed thrust. The results show some evidence of differences between the CD's for cetacean mammals and scombroid fish respectively. Some discussion of this difference is also given.

scholarly journals Power unit float oscillation on the surface of the waves

2021 ◽  
pp. 91-96
Author(s):  
E. A. Bekirov ◽  
D. V. Karkach ◽  
E. R. Murtazaev
Keyword(s):  
Differential Equation ◽  
Power Plant ◽  
Power Unit ◽  
Renewable Energy Sources ◽  
Electrical Energy ◽  
Operating Conditions ◽  
Forced Oscillations ◽  
Wave Power ◽  
Sea Waves ◽  
Integro Differential Equation

One of the urgent tasks of using renewable energy sources is the use of a power unit for converting the energy of sea waves into electrical energy. An important element of the design process of a wave power plant is to carry out mathematical modeling of its operation under various operating conditions to determine the output power and conduct a feasibility study. The process of converting the energy of sea waves into electrical energy for the proposed type of wave power plant is based on forced vertical oscillations of the power unit's float caused by sea waves. The mathematical model of the behavior of the float connected to the generator is based on the integro-differential equation of forced oscillations and makes it possible to determine the dynamics of its oscillations and draw a conclusion about the power taken from the generator connected to the float. The article presents the calculations of the dynamics of the float connected to the generator, the wave equation, the integro-differential equation of the float oscillations, the modeling of the incident wave and the float power unit is carried out. Data on the length, period and height of waves in the Black Sea off the coast of Crimea are used according to official forecasts and observations.

scholarly journals Theoretical Studies of Bounce in Rod-Type Microswitches

2021 ◽  
Vol 346 ◽  
pp. 03034
Author(s):  
E.S. Lyuminarskaya
Keyword(s):  
Differential Equation ◽  
Response Time ◽  
Elastic Element ◽  
Switching Time ◽  
Design Stage ◽  
Theoretical Studies ◽  
Elastic Rod ◽  
Basic Performance ◽  
The Moment ◽  
Improve Reliability

To improve reliability of microswitches, it is necessary to carry out theoretical studies of the switching process both at the moment of switching and at the moment of bouncing. The article presents a dynamic model of microswitches with elastic rod elements, which allows at the design stage to evaluate such basic performance characteristics as response time and contact bounce time. The proposed technique is based on representation of the solution to the differential equation of vibrations of an elastic element in the form of a linear combination of eigenforms and the application of the Bubnov-Galerkin method. Theoretical studies of bounce in a rod microswitch are carried out. It is shown that breakdown precursors of the spacer spring are an increase in the switching time and the time of the first separation in case of bouncing.

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