scholarly journals Dynamic properties of piecewise linear systems with fractional time-delay feedback

2021 ◽  
pp. 146134842110076
Author(s):  
Jianchao Zhang ◽  
Jun Wang ◽  
Jiangchuan Niu ◽  
Yufei Hu
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Analytical Solution ◽  
Goodness Of Fit ◽  
Numerical Solutions ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
State Solution ◽  
Comparison Results

The forced vibration of a single-degree-of-freedom piecewise linear system containing fractional time-delay feedback was investigated. The approximate analytical solution of the system was obtained by employing an averaging method. A frequency response equation containing time delay was obtained by studying a steady-state solution. The stability conditions of the steady-state solution, the amplitude–frequency results, and the numerical solutions of the system under different time-delay parameters were compared. Comparison results indicated a favorable goodness of fit between the two parameters and revealed the correctness of the analytical solution. The effects of the time-delay and fractional parameters, piecewise stiffness, and piecewise gap on the principal resonance and bifurcation of the system were emphasized. Results showed that fractional time delay occurring in the form of equivalent linear dampness and stiffness under periodic variations in the system and influenced the vibration characteristic of the system. Moreover, piecewise stiffness and gap induced the nonlinear characteristic of the system under certain parameters.

scholarly journals On the suitability of the Thorpe-Mason model for Calculating Sublimation of Saltating Snow

2018 ◽  
Author(s):  
Varun Sharma ◽  
Francesco Comola ◽  
Michael Lehning
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Numerical Solutions ◽  
Steady State Solution ◽  
Transient Regime ◽  
State Solution ◽  
Temperature Perturbation ◽  
Alpine Regions ◽  
Drifting Snow ◽  
Tm Model

Abstract. The Thorpe and Mason (TM) model for calculating the mass lost from a sublimating snow grain is the basis of all existing small and large-scale estimates of drifting snow sublimation and the associated snow mass balance of polar and alpine regions. We revisit this model to test its validity for calculating sublimation from saltating snow grains. It is shown that numerical solutions of the unsteady mass and heat balance equations of an individual snow grain reconcile well with the steady-state solution of the TM model, albeit after a transient regime. Using large-eddy simulations (LES), it is found that the residence time of a typical saltating particle is shorter than the period of the transient regime, implying that using the steady state solution might be erroneous. For scenarios with equal air and surface temperatures, these errors range from 26 % for low-wind low-saturation conditions to 38 % for high-wind high-saturation conditions. With a small temperature perturbation of 1 K between the air and the snow surface, the errors due to the TM model are already as high as 100 % with errors increasing for larger temperature perturbations.

Numerical Simulation of Thermal Stratification in the Upper Plenum of Fast Reactor

2013 ◽  
Author(s):  
Seok-Ki Choi ◽  
Tae-Ho Lee
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Thermal Stratification ◽  
Numerical Solutions ◽  
Steady State Solution ◽  
Temporal Variations ◽  
State Solution ◽  
Thermal Mixing ◽  
Commercial Code ◽  
Inlet Conditions

A numerical analysis of the thermal stratification in the upper plenum of the MONJU fast breeder reactor was performed. Calculations were performed for a 1/6 simplified model of the MONJU reactor using the commercial code, CFX-13. To better resolve the geometrically complex upper core structure of the MONJU reactor, the porous media approach was adopted for the simulation. First, a steady state solution was obtained, and the transient solutions were then obtained for the turbine trip test conducted in December 1995. The time dependent inlet conditions for the mass flow rate and temperature were provided by JAEA. Good agreement with the experimental data was observed for the steady state solution. The numerical solution of the transient analysis shows the formation of thermal stratification within the upper plenum of the reactor vessel during the turbine trip test. The temporal variations of temperature were predicted accurately by the present method in the initial rapid coastdown period (∼300 seconds). However, the transient numerical solutions show a faster thermal mixing than that observed in the experiment after the initial coastdown period. A near homogenization of the temperature field in the upper plenum is predicted after about 900 seconds, which is a much shorter-term thermal stratification than the experimental data indicates.

scholarly journals On the suitability of the Thorpe–Mason model for calculating sublimation of saltating snow

2018 ◽  
Vol 12 (11) ◽  
pp. 3499-3509 ◽  
Author(s):  
Varun Sharma ◽  
Francesco Comola ◽  
Michael Lehning
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Numerical Solutions ◽  
Steady State Solution ◽  
Transient Regime ◽  
State Solution ◽  
Alpine Regions ◽  
Drifting Snow ◽  
Tm Model ◽  
Saturation Rate

Abstract. The Thorpe and Mason (TM) model for calculating the mass lost from a sublimating snow grain is the basis of all existing small- and large-scale estimates of drifting snow sublimation and the associated snow mass balance of polar and alpine regions. We revisit this model to test its validity for calculating sublimation from saltating snow grains. It is shown that numerical solutions of the unsteady mass and heat balance equations of an individual snow grain reconcile well with the steady-state solution of the TM model, albeit after a transient regime. Using large-eddy simulations (LESs), it is found that the residence time of a typical saltating particle is shorter than the period of the transient regime, implying that using the steady-state solution might be erroneous. For scenarios with equal initial air and particle temperatures of 263.15 K, these errors range from 26 % for low-wind, low-saturation-rate conditions to 38 % for high-wind, high-saturation-rate conditions. With a small temperature difference of 1 K between the air and the snow particles, the errors due to the TM model are already as high as 100 % with errors increasing for larger temperature differences.

Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka–Volterra System with Time Delay

2015 ◽  
Vol 25 (06) ◽  
pp. 1550089
Author(s):  
Xiaoyuan Chang ◽  
Junjie Wei
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Three Dimensional ◽  
Steady State Solution ◽  
State Solution ◽  
Diffusion System ◽  
Asymptotic Expressions ◽  
The Stability ◽  
System With Time Delay

In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka–Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka–Volterra diffusion system with time delay to illustrate our conclusions.

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

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