Theory, numeric, and experiment studies on stability of two homodromy vibrators in a vibrating system with double rigid frames

2020 ◽  
pp. 107754632093818
Author(s):  
Xueliang Zhang ◽  
Zhenmin Li ◽  
Ming Li ◽  
Dawei Gu ◽  
Bangchun Wen
Keyword(s):  
Mathematical Modeling ◽  
Relative Motion ◽  
Average Method ◽  
Stable States ◽  
Dynamical Characteristics ◽  
Rigid Frames ◽  
Motion Characteristics ◽  
Theoretical Results ◽  
Qualitative Analyses ◽  
Vibrating Systems

The synchronization and stability of two or more vibrators in vibrating systems with double rigid frames are rarely investigated in previous studies. To make up this drawback, we take a dynamical model with double rigid frames driven by two homodromy vibrators, for example the synchronous and stable states of the corresponding system, as well as the relative motion characteristics between the two rigid frames, are analyzed in detail. First, the mathematical modeling of the system is given; the absolute motion and relative motion differential equations of the system are deduced. After that, the theory conditions of implementing synchronization and those of stability are obtained, by using the average method and Hamilton’s principle, respectively. Based on the theoretical results, some numerical qualitative analyses are provided to reveal the coupling dynamical characteristics of the system, and the corresponding ideal working regions are suggested. Finally, experiments are carried out to further examine the validity of the theoretical and numerical results. The present work can offer a reference to design some new vibrating machines such as the considered model.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

Some Remarks on the Identification of Damping Parameters at the Boundary of Vibrating Systems

1995 ◽  
Vol 48 (11S) ◽  
pp. S107-S110
Author(s):  
Peter Hagedorn ◽  
Ulrich Pabst
Keyword(s):  
Mathematical Modeling ◽  
Modal Analysis ◽  
Mechanical Systems ◽  
Experimental Modal Analysis ◽  
Steel Beam ◽  
Modal Data ◽  
Stiffness And Damping ◽  
Parameter Values ◽  
Vibrating Systems

In many cases, vibrating mechanical systems permit a reliable mathematical modeling with parameter values which are reasonably well known beforehand, except for the joints between different subsystems and at the boundaries. The boundary stiffness, which is often assumed as infinite, and the damping at the boundary, which is frequently ignored, are typically not well known. In this note, we discuss the identification of the boundary stiffness and damping parameters from modal data. As an example, we treat an elastic steel beam, for which an experimental modal analysis had been carried out in our laboratory.

scholarly journals Modeling and Kinematics Simulation of a Mecanum Wheel Platform in RecurDyn

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yunwang Li ◽  
Sumei Dai ◽  
Yuwei Zheng ◽  
Feng Tian ◽  
Xucong Yan
Keyword(s):  
Virtual Prototype ◽  
Mobile System ◽  
Design Quality ◽  
Simulation Experiments ◽  
Motion Models ◽  
Kinematics Simulation ◽  
Simulation Results ◽  
Mecanum Wheel ◽  
Motion Characteristics ◽  
Theoretical Results

The innovative method of modeling and kinematics simulation in RecurDyn are proposed, taking a Mecanum wheel platform(MWP) for omnidirectional wheelchair as research object. In order to study the motion characteristics and mobile performance of the MWP, the virtual prototype simulation model is established in SolidWorks, and virtual prototype simulation is carried out in RecurDyn. The experience of simulation for the MWP in RecurDyn is introduced, and the simulation steps and points for attention are described detailedly. The working states of the mobile system in real environment have been simulated through virtual simulation experiments. Four typical motion models including moving forward, moving laterally, moving laterally in the direction of 45°, and rotation have been simulated in RecurDyn. The simulation results exactly reflect the motion of the MWP. By comparing the simulation results with the theoretical results, there are acceptable errors that are relatively less overall in the simulation results. The simulation results can be used to predict the performance of the platform and evaluate the design rationality, and design quality can be improved according to the exposed problem. This paper can provide reference for the simulation of mobile platform by using RecurDyn.

scholarly journals The Impact of Cost Uncertainty on Cournot Duopoly Game with Concave Demand Function

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
S. S. Askar
Keyword(s):  
Optimization Problem ◽  
Demand Function ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Worst Case ◽  
Dynamical Characteristics ◽  
Inflection Points ◽  
The Cost ◽  
The Impact ◽  
Theoretical Results

It is reported in the literature that the most fundamental idea to address uncertainty is to begin by condensing random variables. In this paper, we propose Cournot duopoly game where quantity-setting firms use nonlinear demand function that has no inflection points. A random cost function is introduced in this model. Each firm in the model wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the cost. To handle this multiobjective optimization problem, the expectation and worst-case approaches are used. A model of two rational firms that are in competition and produce homogenous commodities is introduced using an unknown demand function. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation, and chaos are investigated. Complete stability and bifurcation analysis are provided. The obtained theoretical results are verified by numerical simulation.

Research Regarding the Dynamic Behavior of Linear Hydraulic Servo-Systems

2013 ◽  
Vol 325-326 ◽  
pp. 480-485
Author(s):  
Petrin Drumea ◽  
Corneliu Cristescu ◽  
Catalin Dumitrescu ◽  
Iulian Dutu ◽  
Ioana Ilie
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Dynamic Behavior ◽  
Theoretical Research ◽  
Scientific Interest ◽  
Servo Systems ◽  
Hydraulic Motors ◽  
Hydraulic Servo ◽  
Computer Numerical Simulation ◽  
Theoretical Results

The paper presents the theoretical results of extensive research on the dynamic behavior of linear hydraulic motors, carried out in INOE 2000-IHP, in the framework of the NUCLEU Programmer. The research has been conducted both theoretically and experimentally, but, in this paper, is presented only the theoretical research. Theoretical research has taken place with the modern means of mathematical modeling and computer numerical simulation. The article presents some theoretical interested results obtained in the research, results that are of real scientific interest, but, also, with practical value through their use in the design of fluid power components and equipments.

Parametric Research on Micro-Zigzag Slot Mechanism in OICW

2011 ◽  
Vol 483 ◽  
pp. 699-704 ◽  
Author(s):  
Chuan Qin Liu ◽  
Wen Zhong Lou ◽  
Long Fei Zhang ◽  
Yong Jia Lv
Keyword(s):  
Mathematic Model ◽  
Rectangular Pulse ◽  
Structural Parameter ◽  
Delayed Effect ◽  
Linear Dynamic ◽  
Simulation Results ◽  
Motion Characteristics ◽  
Acceleration Signals ◽  
Theoretical Results ◽  
Simulation Condition

This paper describes the delayed effect on the motion characteristics of the slider in the S&A mechanism resulting from the micro-zigzag slot used in OICW (Objective Individual Combat Weapon) and studies its influence on the ability of filtering transient acceleration signals. Firstly, we established the mathematic model of the slider when the S&A mechanism was loaded by the rectangular pulse acceleration according to the Rigid Dynamic Mechanics Theory and got its analytical solution by using MATLAB. Secondly, to verify the feasibility of this micro-zigzag slot mechanism, we adopted two different kinds of acceleration loading curves, after the non-linear dynamic mechanics simulation on it by using ANSYS/LS-DYNA, displacement and velocity curves of the slider were calculated. Then, to find which structural parameter playing more important role in affecting the characteristics of micro-zigzag slot, we adopted Single-variable Method to study its structural parameter under the same simulation condition. The simulation results we got were almost consistent with the theoretical results. The parametric research of the micro-zigzag slot lays certain a foundation on the research of MEMS system.

scholarly journals MOVEMENT OF THE PARTICLE ON THE INTERNAL SURFACE OF THE SPHERICAL SEGMENT ROTATING ABOUT A VERTICAL AXIS

2020 ◽  
pp. 79-88
Author(s):  
Sergiy Pylypaka ◽  
Victor Nesvidomin ◽  
Tatiana Volina ◽  
Larysa Sirykh ◽  
Liudmyla Ivashyna
Keyword(s):  
Numerical Methods ◽  
Experimental Research ◽  
Relative Motion ◽  
Particle Motion ◽  
Internal Surface ◽  
Vertical Axis ◽  
Relative Displacement ◽  
Spherical Segment ◽  
Velocity Changes ◽  
Theoretical Results

The particle relative motion on a spherical segment rotating about a vertical axis was considered in the article. The differential equations of the relative displacement of a particle were completed and solved by numerical methods. The relative and absolute trajectories of particle motion and graphs of relative and absolute velocity changes were constructed. The regularity of particle motion as it is lifted over the surface was found out. The conducted experimental research has confirmed the received theoretical results.

A MATHEMATICAL FRAMEWORK EXHIBITING THE EMERGENCE OF DYNAMIC EXPANSION OF TASK REPERTOIRE IN PHEIDOLE DENTATA

2016 ◽  
Vol 24 (02n03) ◽  
pp. 217-235 ◽  
Author(s):  
JASON M. GRAHAM ◽  
IVAN L. SIMPSON-KENT ◽  
MARC A. SEID
Keyword(s):  
Mathematical Modeling ◽  
Age Groups ◽  
Theoretical Work ◽  
Clear Understanding ◽  
Mathematical Framework ◽  
Modeling Framework ◽  
Age Related ◽  
Pheidole Dentata ◽  
Underlying Mechanisms ◽  
Theoretical Results

The division of labor (DOL) and task allocation (TA) among groups of ants living in a colony is thought to be highly efficient, and key to the robust survival of a colony. A great deal of experimental and theoretical work has been done toward gaining a clear understanding of the evolution of, and underlying mechanisms of these phenomena. Much of this research has utilized mathematical modeling. Here we continue this tradition by developing a mathematical model for a particular aspect of TA, known as age-related repertoire expansion, that has been observed in the minor workers of the ant species Pheidole dentata. In fact, we present a relatively broad mathematical modeling framework based on the dynamics of the frequency with which members of specific age groups carry out distinct tasks. We apply our modeling approach to a specific TA scenario, and compare our theoretical results with experimental data. It is observed that the model predicts perceived behavior, and provides a possible explanation for the aforementioned experimental results.

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