scholarly journals Input shaping control of a flexible cantilever beam excited by a moving hub

2020 ◽  
Vol 3 (2) ◽  
pp. First
Author(s):  
Quoc Chi Nguyen ◽  
Nguyen Tri Giang Vu ◽  
Phuong Tung Pham
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Cantilever Beam ◽  
High Speed ◽  
Beam Theory ◽  
Flexible Beam ◽  
Structural Element ◽  
Unknown Parameters ◽  
The Mathematical Model

Introduction: A cantilever beam is a well-known structural element in engineering, which is only fixed at one end. This structure can be used to describe a manipulator, whose stiffness is large to ensure rigidity and stability of the system. A flexible cantilever beam provides a light-weight structure and high cost efficiency but generates vibration under high-speed positioning. In this paper, we aim to control the vibratory behavior of a flexible cantilever beam attached to a moving hub. Method: The mathematical model of the flexible beam is described by partial differential equations (PDEs) using Euler-Bernoulli beam theory. Then, The PDE model is approximated by using the Galerkin method, which is resulted in a set of ordinary differential equations (ODEs). Experiment is used to determine unknown parameters of the system to complete the model. The ODE model enables the control design of three input shapers: (i) Zero-Vibration (ZV), (ii) Zero-Vibration-Derivative (ZVD), and (iii) Zero-Vibration-Derivative-Derivative (ZVDD), which are employed to drive the flexible beam to the desired position and to reduce vibrations of the beam. Results and conclusion: The dynamic model is obtained in term of ordinary differential equations. Unknown parameters of the system are determined by experimental process. Various controllers are designed to eliminate the vibration of the beam. The simulation is applied to predict the dynamic response of the beam to verify the designed controllers numerically. Experiment shows the validity of the mathematical model through the consistency between the simulation and experimental data and the effectiveness of the controllers for the real system. These controllers show several advantages such as no need of extra equipment; the positioning controller is intact, which means it may be applied to many existing systems.

SELF-SIMILAR PROBLEMS FOR MODELING THE SURFACE CHEMICAL REACTIONS WITH THE GRAVITATION

1998 ◽  
Vol 3 (1) ◽  
pp. 25-32
Author(s):  
Jânis Cepîtis ◽  
Harijs Kalis
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reactions ◽  
Glass Fibre ◽  
Surface Chemical ◽  
Self Similar ◽  
Surface Chemical Reactions ◽  
The Mathematical Model

The mathematical model of a chemical reaction which takes place on the surface of the uniformly moving vertically imbedded glass fibre material is considered. The effect of gravitation is taken into account. Boussinesq's and boundary layer fittings allow to derive boundary value problems for self‐similar systems of ordinary differential equations.

Mathematical modeling of articulated passenger train spatial vibrations

2021 ◽  
Vol 2021 (2) ◽  
pp. 91-99
Author(s):  
O. Markova ◽  
◽  
H. Kovtun ◽  
V. Maliy ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Ride Quality ◽  
Railway Transport ◽  
Passenger Train ◽  
Wide Range ◽  
Random Track Irregularities ◽  
The Mathematical Model

The problem of high-speed railway transport development is important for Ukraine. In many countries articulated trains are used for this purpose. As the connections between cars in such a train differ from each other, to investigate its dynamic characteristics not a separate car, but a full train vibrations model is necessary. The article is devoted to the development of the mathematical model for articulated passenger train spatial vibrations. The considered train consists of 7 cars: one motor-car, one transitional car, three articulated cars, one more transitional car and again one motor-car. Differential equations of the train motion along the track of arbitrary shape are set in the form of Lagrange’s equations of the second kind. All the necessary design features of the vehicles are taken into account. Articulated cars have common bogies with adjoining cars and a transfer car and the cars are united by the hinge. The operation of the central hinge between two cars is modeled using springs and dampers acting in the horizontal and vertical directions. Four dampers between two adjacent car-bodies act as dampers for pitching and hunting and are represented in the model by viscous damping. The system of 257 differential equations of the second order is set, which describes the articulated train motion along straight, curved, and transitional track segments with taking into account random track irregularities. On the basis of the obtained mathematical model the algorithm and computational software has been developed to simulate a wide range of cases including all possible combinations of parameters for the train elements and track technical state. The study of the train self-exited vibrations has shown the stable motion in all the range of the considered speeds (40 km/h – 180 km/h). The results obtained at the train motion along the track maintained for the speedy motion have shown that all the dynamic characteristics and ride quality index insure train safe motion and comfortable conditions for the travelling passengers.

scholarly journals ВИКОРИСТАННЯ МОДЕЛІ НЕЛІНІЙНОЇ ДИНАМІКИ ДЛЯ АНАЛІЗУ ВПЛИВУ СИСТЕМИ УПРАВЛІННЯ ЗНАННЯМИ НА РЕАЛІЗАЦІЮ ВИСОКОТЕХНОЛОГІЧНИХ ПРОЕКТІВ

2019 ◽  
pp. 76-82
Author(s):  
Василь Михайлович Вартанян ◽  
Дар'я Олександрівна Штейнбрехер
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Knowledge Management ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Management System ◽  
Knowledge Management System ◽  
Project Implementation ◽  
The Impact ◽  
The Mathematical Model

The article determines that at the present stage of the project management development in information-oriented society, the decision-making process on the efficiency of the knowledge management system assessment is complicated, due to the lack of approaches that determine the impact of the system on the project implementation. The article presents the main results of the analysis of the current state of the problem of modeling the knowledge management system of high-tech projects, which helped to establish that one of the factors of the introduction of an effective system of knowledge preservation is the ability to assess the impact of the system on the project environment.In order to solve the problem, the mathematical model of nonlinear dynamics for the analysis of the influence of knowledge management system on the project based on the Bulirsch–Stoer method was proposed, it is possible to evaluate the influence of elements of the knowledge management system on the projected stages of the project implementation and to calculate the duration of the project taking into account their influence. The mathematical model of nonlinear dynamics for the analysis of the influence of the knowledge management system on the Bulirsch–Stoer method is given to evaluate the influence of elements of the knowledge management system on the projected implementation stages and to calculate the duration of the project, taking into account their impact. Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method, to obtain numerical solutions to ordinary differential equations (ODEs) with high accuracy and comparatively little computational effort. The step-by-step tracking of the knowledge management system impact on the project development will allow the project manager to predict both its successful completion and the risks of deviation from the scheduled time due to the loss of critical knowledge, which largely stems from the successful implementation of the project.Further research will be aimed at developing a model that allows us to assess the profitability of the system in the design environment, based on the results of the proposed mathematical model.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Research on the Performance Simulation of the Transmission System of Loader with Secondary Regulating Technique

2010 ◽  
Vol 426-427 ◽  
pp. 299-302
Author(s):  
Fa Ye Zang
Keyword(s):  
Mathematical Model ◽  
Fuzzy Control ◽  
Energy Saving ◽  
High Speed ◽  
Transmission System ◽  
Performance Simulation ◽  
Constant Torque ◽  
Braking Torque ◽  
The Mathematical Model ◽  
Inertial Energy

Based on deeply analyzing the working principles and energy-saving theory of loader secondary regulating transmission system, regenerating the transmission system’s inertial energy by controlling constant torque was put forward. Considering large changes of the parameters of the transmission system and its non-linearity, a fuzzy control was adopted to control the transmission system, and the mathematical model of the system was established, then the simulations of the performance of the transmission system has been conducted. The conclusion was made that the inertial energy can be reclaimed and reused in the system by the application of the secondary regulation technology, and braking by controlling constant torque is stable, it can ensure the security of braking at high speed and also permits changing the efficiency of recovery by changing the braking torque. The system’s power has been reduced and energy saving has been achieved.

Increasing the mobility of a high-speed tracked vehicle based on a controlled skid algorithm

2020 ◽  
pp. 29-33
Author(s):  
S. V. Kondakov ◽  
O.O. Pavlovskaya ◽  
I.D. Ivanov ◽  
A.R. Ishbulatov
Keyword(s):  
Mathematical Model ◽  
Dynamic Stability ◽  
Simulation Modeling ◽  
Automatic System ◽  
High Speed ◽  
Control Algorithm ◽  
Loss Of Stability ◽  
Tracked Vehicle ◽  
Hydrostatic Transmission ◽  
The Mathematical Model

A method for controlling the curvilinear movement of a high-speed tracked vehicle in a skid without loss of stability is proposed. The mathematical model of the vehicle is refined. With the help of simulation modeling, a control algorithm is worked out when driving in a skid. The effectiveness of vehicle steering at high speed outside the skid is shown. Keywords: controlled skid, dynamic stability, steering pole displacement, hydrostatic transmission, automatic system, fuel supply. [email protected]

scholarly journals The analysis of flutter characteristics based on generalized parameters of eigen modes of vibrations

2021 ◽  
pp. 95-102
Author(s):  
K. I Barinova ◽  
A. V Dolgopolov ◽  
O. A Orlova ◽  
M. A Pronin
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Dynamic Pressure ◽  
Mode Shapes ◽  
Scaled Model ◽  
Design Specifications ◽  
Operation Conditions ◽  
Flutter Analysis ◽  
Generalized Parameters ◽  
The Mathematical Model

Flutter numerical analysis of a dynamically scaled model (DSM) of a high aspect ratio wing was performed using experimentally obtained generalized parameters of eigen modes of vibrations. The DSM is made of polymer composite materials and is designed for aeroelastic studies in a high-speed wind tunnel. As a result of the analysis, safe operation conditions (flutter limits) of the DSM were determined. The input data to develop the flutter mathematical model are DSM modal test results, i.e. eigen frequencies, mode shapes, modal damping coefficients, and generalized masses obtained from the experiment. The known methods to determine generalized masses have experimental errors. In this work some of the most practical methods to get generalized masses are used: mechanical loading, quadrature component addition and the complex power method. Errors of the above methods were analyzed, and the most reliable methods were selected for flutter analysis. Comparison was made between the flutter analysis using generalized parameters and a pure theoretical one based on developing the mathematical model from the DSM design specifications. According to the design specifications, the mathematical model utilizes the beam-like schematization of the wing. The analysis was performed for Mach numbers from 0.2 to 0.8 and relative air densities of 0.5, 1, 1.5. Comparison of the two methods showed the difference in critical flutter dynamic pressure no more than 6%, which indicates good prospects of the flutter analysis based on generalized parameters of eigen modes.

Center-Focus Problem for Discontinuous Planar Differential Equations

2003 ◽  
Vol 13 (07) ◽  
pp. 1755-1765 ◽  
Author(s):  
Armengol Gasull ◽  
Joan Torregrosa
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Critical Point ◽  
Limit Cycles ◽  
New Method ◽  
Polar Coordinates ◽  
Mechanical Problem ◽  
Weak Focus ◽  
Elastic Walls

We study the center-focus problem as well as the number of limit cycles which bifurcate from a weak focus for several families of planar discontinuous ordinary differential equations. Our computations of the return map near the critical point are performed with a new method based on a suitable decomposition of certain one-forms associated with the expression of the system in polar coordinates. This decomposition simplifies all the expressions involved in the procedure. Finally, we apply our results to study a mathematical model of a mechanical problem, the movement of a ball between two elastic walls.

scholarly journals Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere

Molecules ◽  
2020 ◽  
Vol 25 (11) ◽  
pp. 2694
Author(s):  
Amir Abbas ◽  
Muhammad Ashraf ◽  
Yu-Ming Chu ◽  
Saqib Zia ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mixed Convection ◽  
Computational Study ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Partial Differential ◽  
Primitive Form ◽  
The Mathematical Model

The main goal of the current work was to study the coupled mechanism of thermophoretic transportation and mixed convection flow around the surface of the sphere. To analyze the characteristics of heat and fluid flow in the presence of thermophoretic transportation, a mathematical model in terms of non-linear coupled partial differential equations obeying the laws of conservation was formulated. Moreover, the mathematical model of the proposed phenomena was approximated by implementing the finite difference scheme and boundary value problem of fourth order code BVP4C built-in scheme. The novelty point of this paper is that the primitive variable formulation is introduced to transform the system of partial differential equations into a primitive form to make the line of the algorithm smooth. Secondly, the term thermophoretic transportation in the mass equation is introduced in the mass equation and thus the effect of thermophoretic transportation can be calculated at different positions of the sphere. Basically, in this study, some favorite positions around the sphere were located, where the velocity field, temperature distribution, mass concentration, skin friction, and rate of heat transfer can be calculated simultaneously without any separation in flow around the surface of the sphere.

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

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