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.

scholarly journals Mathematical model of the dynamics of business development

2020 ◽  
pp. 18-34
Author(s):  
Alexander Sklyar
Keyword(s):  
Differential Equation ◽  
Business Development ◽  
Economic Behavior ◽  
Model Data ◽  
Political Factors ◽  
Noise Component ◽  
The Moment ◽  
Actual Return ◽  
Investment Process ◽  
Production Capacities

The subject of this research is the model of business development that describes the dependence of ongoing volume of production from previous investments and intensity of wear of production capacities. The investment process is characterized by a delay between the moment of investment, actual return and its continuation, gradual decrease in the level of return, and discreetness of investments. In the process of modeling, discrete investment were replaced by an integral, which leads to integral-differential equation, and in terms of facile assumption to the linear standard differential equation of second order or their system, solved by the disharmonious fluctuations on the background of an aperiodic trend. As the method of analysis of correspondence of the model data with the actual dynamics of business development, the research utilizes computational solution of the emerging differential equations. Comparison of the model data with the known statistics reveals their adequacy to the current economic processes. Statistical data contains noise component, which consists of various economic and political factors and principally limits the precision of forecasting. Differences in the length of fluctuation periods by industries impedes analysis of the economic behavior as a whole. At the same time, forecast of crisis phenomena that emerge in superposition of the phases of industry fluctuations can be executed with sufficient level of precision.

scholarly journals The ruin problem for a Wiener process with state-dependent jumps

2020 ◽  
Vol 16 (1) ◽  
pp. 13-23
Author(s):  
M. Lefebvre
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Jump Diffusion ◽  
Moment Generating Function ◽  
Continuous Part ◽  
State Dependent ◽  
The Moment ◽  
First Time

AbstractLet X(t) be a jump-diffusion process whose continuous part is a Wiener process, and let T (x) be the first time it leaves the interval (0,b), where x = X(0). The jumps are negative and their sizes depend on the value of X(t). Moreover there can be a jump from X(t) to 0. We transform the integro-differential equation satisfied by the probability p(x) := P[X(T (x)) = 0] into an ordinary differential equation and we solve this equation explicitly in particular cases. We are also interested in the moment-generating function of T (x).

Determination of the Buckling Load of Struts with Successive Approximations

1943 ◽  
Vol 47 (387) ◽  
pp. 103-105
Author(s):  
J. Ratzersdorfer
Keyword(s):  
Differential Equation ◽  
Compressive Force ◽  
Buckling Load ◽  
Moment Of Inertia ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Exact Determination ◽  
The Moment ◽  
Image Position

In cases of tapered struts with hinged or built-in ends where the exact determination of the buckling load is complicated it may be useful to apply a method of successive approximations.Let us first consider a bar of the length l with hinged ends under the action of the compressive force P. The differential equation of the bending line becomeswhere v is the deflection at the section u, v with the moment of inertia I (u) and E is Young's modulus. At the ends of the bar the deflection v is equal to zero (Fig. I).

Separating Perception Time from Response Time: The Slope Transition Paradigm

Perception ◽  
10.1068/p3304 ◽  
2002 ◽  
Vol 31 (3) ◽  
pp. 323-339 ◽  
Author(s):  
Ethel Matin ◽  
David C Nofer ◽  
Lisa Gische
Keyword(s):  
Response Time ◽  
Psychological Refractory Period ◽  
Visual Presentation ◽  
Perceptual Processing ◽  
Capacity Limits ◽  
Set Size ◽  
Perception Time ◽  
The Subject ◽  
The Moment ◽  
Set Size Effects

This paper describes the slope transition paradigm (STP), a variant of rapid serial visual presentation (RSVP) that separates early (perceptual) processing time from total response time. The paradigm is based on a very simple idea: provide varying amounts of time for perceptual processing and find the moment when the subject begins to waste time waiting for more data. That moment is a measure of how much time was actually needed. The method was used in two experiments. Results are discussed in relation to set-size effects, perceptual capacity limits, attentional dwell times, and some related neurophysiological findings. The method appears to tap aspects of information processing that differ from those tapped in studies of the psychological refractory period, the attentional blink, and repetition blindness.

An optimum design procedure for both serial and parallel manipulators

2007 ◽  
Vol 221 (7) ◽  
pp. 829-843 ◽  
Author(s):  
G Carbone ◽  
E Ottaviano ◽  
M Ceccarelli
Keyword(s):  
Optimization Problem ◽  
Design Procedure ◽  
Parallel Manipulators ◽  
Optimality Criteria ◽  
Design Stage ◽  
Multi Objective Optimization ◽  
Numerical Examples ◽  
Design Optimality ◽  
Basic Performance ◽  
Alternative Solutions

Serial and parallel manipulators can be used in different manipulative tasks when their peculiarities in kinematic and dynamic behaviours are properly considered from the design stage. The basic performance in workspace, mobility constraints, and stiffness makes them alternative solutions and not competitive manipulator chains. Thus, it is convenient to deduce a common design procedure that considers common design criteria, but specific numerical evaluations. In this paper, a multi-objective optimization problem has been proposed to formulate a unique design procedure that takes into account the contradicting design optimality criteria in terms of suitable general algorithms for workspace volumes, Jacobian matrices, and compliant displacements. Numerical examples are reported to show not just the feasibility but also the numerical efficiency of the proposed formulations.

scholarly journals RESEARCH OF TECHNICAL CHARACTERISTICS OF NEW TYPES OF COUPLINGS

2020 ◽  
pp. 113-121
Author(s):  
Oleksii Tokarchuk ◽  
Yurii Polievoda
Keyword(s):  
Elastic Element ◽  
Rational Design ◽  
Experimental Studies ◽  
Bending Moment ◽  
Operational Reliability ◽  
Modern Technology ◽  
Operating Conditions ◽  
The Moment ◽  
Working Bodies ◽  
Moment Of Resistance

Dynamic loads that occur during the operation of existing couplings cause significant shock loads, which leads to rapid wear of the surfaces of the couplings and shortens the service life. Modern technology faces the task of improving the operational reliability of the working bodies and drives of machines. One way to solve this problem is to develop and use high-precision and low-dynamic safety couplings. In this regard, the question of developing new designs of safety couplings that reduce impact loads and increase the reliability and durability of machinery is relevant. The synthesis of structural and kinematic schemes of ball, cam and planetary safety couplings, the method of their calculation in combination with the nature of the change in the moment of resistance on the working body of the equipment. The article conducts a set of theoretical and experimental studies to determine their rational design, kinematic and dynamic parameters that will satisfy the operating conditions of machines and mechanisms. A force analysis of the elastic element (ring spring) was performed. The scheme of loading of an elastic element by two forces and other settlement schemes are constructed, namely: equivalent system; force diagrams for determining the load torque; force schemes for determining the unit moment; schemes of total bending moment; force schemes to determine the total unit moment. During static experimental studies of the developed ball safety couplings, the nature of their operation was established, the maximum torque at the two stages of operation of the couplings was determined and a comparative analysis between the results of theoretical and experimental studies was performed. The positive results of experimental researches of the developed coupling and theoretical positions which can be applied to a substantiation and a choice of rational parameters of the developed designs of couplings and their engineering designing were confirmed.

scholarly journals То the synchronous work of pulsed sources of seismic waves

2019 ◽  
pp. 75-79
Author(s):  
S. P. Ekomasov
Keyword(s):  
Control System ◽  
Response Time ◽  
Half Space ◽  
Seismic Waves ◽  
Time Interval ◽  
Shock Interaction ◽  
Seismic Efficiency ◽  
Pulse Type ◽  
The Stability ◽  
The Moment

Researches have been made with the use of a hydropneumatic source of seismic waves. This source on the realized efforts of the shock interaction with a soil half-space considerably exceeds all known designs of radiators (sources) of pulse type. In this regard it shows higher seismic efficiency. The most important characteristic of the work of the pulse sources of seismic waves is a stability of the response time — a time interval from the moment of giving of a signal for producing of the blow until the very blow. Only with the achievement of the necessary stability the work in the mode of grouping of sources and accumulation of signals is possible. Features of the formation of response time of a hydropneumatic source are given. The analysis of the assessment of the parameters of synchronism of the pulse sources is made by a modem control system of their work. An influence of the rigidity of the soil on the assessment of stability of the response time and synchronism is shown. The system of the assessment of the stability used in the existing pulse sources at its application does not reflect the actual stability of response time in the radiators possessing a big force of blow.

scholarly journals Spectral Curves for the Triple Reduced Product of Coadjoint Orbits for SU(3)

2018 ◽  
pp. 611-622 ◽  
Author(s):  
Jacques Hurtubise ◽  
Lisa Jeffrey ◽  
Steven Rayan ◽  
Paul Selick ◽  
Jonathan Weitsman
Keyword(s):  
Differential Equation ◽  
Higgs Field ◽  
Moment Map ◽  
Circle Action ◽  
Coadjoint Orbits ◽  
Genus Zero ◽  
Spectral Curves ◽  
Hitchin System ◽  
The Moment

This chapter gives an identification of the triple reduced product of three coadjoint orbits in SU(3) with a space of Hitchin pairs over a genus zero curve with three punctures, where the residues of the Higgs field at the punctures are constrained to lie in fixed coadjoint orbits. Using spectral curves for the corresponding Hitchin system, the chapter identifies the moment map for a Hamiltonian circle action on the reduced product. Finally, the chapter makes use of results from Adams, Harnad and Hurtubise to find Darboux coordinates and a differential equation for the Hamiltonian.

On the Nonlinear Differential Equation for Beam Deflection: EI d 2 y / dx 2 = M ( x ) [ 1 + ( dy / dx ) 2 ] 3 ⁄ 2

1955 ◽  
Vol 22 (2) ◽  
pp. 245-248
Author(s):  
E. J. Scott ◽  
D. R. Carver
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Nonlinear Differential Equation ◽  
Beam Deflection ◽  
Beam Equation ◽  
Nonlinear Beam ◽  
Independent Variable ◽  
The Moment

Abstract A general solution of the nonlinear beam equation is given for all problems in which the moment can be expressed as a function of the independent variable alone.

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