The Study of the Initial State of Cable-Net Structure Reflector for the FAST

By using the variational principle to set up the mathematical model of the reflector for the FAST, we can get the node location of the cable-net and tension of the main cable by solving highly nonlinear equations of the mathematical model. A new layer-by-layer substitution approach has been proposed for solving the highly nonlinear equations, through the calculation and simulation it verifies the correctness of this method.

Bending of Thermoviscoelastic Functionally Graded Materials Beams

10.4028/www.scientific.net/amr.503-504.305 ◽

2012 ◽

Vol 503-504 ◽

pp. 305-308

Author(s):

Ming Lu Wang ◽

Gao Feng Wei

Keyword(s):

Mathematical Model ◽

Variational Principle ◽

Laplace Transformation ◽

Transformation Method ◽

Functionally Graded ◽

Plane Section ◽

Graded Materials ◽

Set Up ◽

The Mathematical Model ◽

Laplace Transformation Method

According to the constitutive relation of linear thermovisoelasticity, with the help of Laplace transformation method and the introduction of structure functions and thermal functions, the mathematical model and its corresponding variational principle for thermoviscoelastic FGM beams are set up on the basis of the assumption that plane section remains plane and normal to the beam axis. Using Laplace transformation method, the deflection and the stress distribution are discussed.

Research on Dynamic Balance Method of Precision Centrifuge

10.4028/www.scientific.net/amr.945-949.777 ◽

2014 ◽

Vol 945-949 ◽

pp. 777-780

Author(s):

Tao Liu ◽

Yong Xu ◽

Bo Yuan Mao

Keyword(s):

Mathematical Model ◽

Balance Control ◽

Dynamic Balance ◽

Dynamic Balancing ◽

Structure Characteristics ◽

Balance System ◽

Simulation Results ◽

Set Up ◽

System Controller ◽

Firstly, according to the structure characteristics of precision centrifuge, the mathematical model of its dynamic balancing system was set up, and the dynamic balancing scheme of double test surfaces, double emendation surfaces were established. Then the dynamic balance system controller of precision centrifuge was designed. Simulation results show that the controller designed can completely meet the requirements of precision centrifuge dynamic balance control system.

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

Study on the working state of the five hundred-meter aperture spherical telescope using step-wise assignment method

10.1177/0954406214533528 ◽

2014 ◽

Vol 229 (2) ◽

pp. 316-324 ◽

Cited By ~ 1

Author(s):

Yu Liu ◽

Feng Gao

Keyword(s):

Nonlinear Equations ◽

Analytical Solutions ◽

Driving Mechanism ◽

Initial Value ◽

Unknown Parameters ◽

Support Structure ◽

Assignment Method ◽

New Type ◽

Set Up ◽

The working state of the five hundred-meter aperture spherical telescope (FAST) is solved using the step-wise assignment method. In this paper, the mathematical model of the cable-net support structure of the FAST is set up by the catenary equation. There are a large number of nonlinear equations and unknown parameters of the model. The nonlinear equations are solved by using the step-wise assignment method. The method is using the analytical solutions of the cable-net equations of one working state as the initial value for the next working state, from which the analytical solutions of the nonlinear equations of the cable-net for each working state of the FAST and the tension and length of each driving cable can be obtained. The suggested algorithm is quite practically well suited to study the working state of the cable-net structures of the FAST. Also, the working state analysis result of the cable-net support structure of a reduced model of the cable-net structure reflector for the FAST is given to verify the reliability of the method. In order to show the validity of the method, comparisons with another algorithm to set the initial value are presented. This method has an important guiding significance to the further study on the control of the new type of flexible cable driving mechanism, especially the FAST.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

Volume 6B: 18th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc2001/vib-21555 ◽

2001 ◽

Author(s):

Jia Xiaohong ◽

Ji Linhong ◽

Jin Dewen ◽

Zhang Jichuan

Keyword(s):

Mathematical Model ◽

Equations Of Motion ◽

Experimental Studies ◽

Active System ◽

New Concepts ◽

Sliding Joint ◽

New Type ◽

Set Up ◽

The Mathematical Model ◽

Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Parametric Variational Principle of Viscoplastic Lubrication Model

Journal of Tribology ◽

10.1115/1.2920942 ◽

1992 ◽

Vol 114 (4) ◽

pp. 731-735 ◽

Cited By ~ 13

Author(s):

C. W. Wu ◽

W. X. Zhong ◽

L. X. Qian ◽

L. C. Hu ◽

S. M. Sun

Keyword(s):

Mathematical Model ◽

Mathematical Method ◽

Variational Principle ◽

Original Problem ◽

Engineering Application ◽

Tangential Velocity ◽

Control Vector ◽

Parametric Variational Principle ◽

Variational Process ◽

An effective mathematical method to deal with the viscoplastic lubrication model is presented here by applying the parametric variational principle (Zhong, 1985). The plastic slippage of lubricant would occur at the lubricated surfaces under isothermal lubrication. The boundary tangential velocity, therefore, can be taken as the parametric vector (or the control vector) in variational process. The mathematical model of the original problem is finally reduced to a complementarity problem. The algorithm presented in this paper is simple and reliable and shows promise in engineering application.

Numerical Analysis of Heat and Mass Transfer Performance of the Packed-Type Parallel Flow Dehumidifier

10.4028/www.scientific.net/amr.989-994.3100 ◽

2014 ◽

Vol 989-994 ◽

pp. 3100-3104

Author(s):

Rui Hang Zhang ◽

Zi Ye Wang ◽

Run Ping Niu

Keyword(s):

Mathematical Model ◽

Mass Transfer ◽

Heat And Mass Transfer ◽

Parallel Flow ◽

Transfer Performance ◽

Transfer Coefficients ◽

Simulation Results ◽

Set Up ◽

The Impact ◽

TA mathematical model describing heat and mass transfer performance of packed-type parallel flow dehumidifier was set up. The numerical solution of differential equations was derived. Taking the heat and mass transfer coefficients obtained by experiments as the input parameters of the model, the impact of solution inlet parameters on outlet parameter of air was described. The simulation results indicated that the mathematical model could be used to predict the performance of liquid dehumidification. The results showed that the mathematical model can be of great value in the design and improvement of dehumidifier.

WAVE ATTENUATION AND WAVE SET-UP ON A COASTAL REEF

Coastal Engineering Proceedings ◽

10.9753/icce.v17.27 ◽

1980 ◽

Vol 1 (17) ◽

pp. 27 ◽

Cited By ~ 4

Author(s):

Franciscus Gerritsen

Keyword(s):

Mathematical Model ◽

Wave Attenuation ◽

Scale Effects ◽

Shallow Reef ◽

Laboratory Investigations ◽

Deep Water Wave ◽

Set Up ◽

The University ◽

Incident Waves ◽

In attempting to specify criteria for the design of structures on coastal reefs, it was found that no adequate method existed to derive those criteria from the deep water wave conditions. In order to fill the gap, a program of measurements and analysis was initiated at the University of Hawaii. The program consisted of prototype and laboratory measurements. Great emphasis was placed on reliable field data, which were collected on Ala Moana Reef, in Honolulu. Laboratory investigations on the behavior of waves on shallow reefs are subject to scale effects; verification from field observations is required to obtain reliable results. As a result of this study, a mathematical model was developed for the calculation of wave attenuation and wave set-up on a shallow reef, using the incident waves in the ocean as boundary conditions. This paper discusses the general behavior of waves approaching a shallow reef and presents some essential characteristics of the mathematical model. The study is limited to waves approaching the shoreline at right angles. The results of this study can be extended to breakwaters with wide, submerged berms.

Working Characteristics of Variable Intake Valve in Compressed Air Engine

The Scientific World JOURNAL ◽

10.1155/2014/498934 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Qihui Yu ◽

Yan Shi ◽

Maolin Cai

Keyword(s):

Mathematical Model ◽

Energy Utilization ◽

Utilization Efficiency ◽

Compressed Air ◽

Maximum Output ◽

Output Torque ◽

Good Consistency ◽

Intake Pressure ◽

Set Up ◽

A new camless compressed air engine is proposed, which can make the compressed air energy reasonably distributed. Through analysis of the camless compressed air engine, a mathematical model of the working processes was set up. Using the software MATLAB/Simulink for simulation, the pressure, temperature, and air mass of the cylinder were obtained. In order to verify the accuracy of the mathematical model, the experiments were conducted. Moreover, performance analysis was introduced to design compressed air engine. Results show that, firstly, the simulation results have good consistency with the experimental results. Secondly, under different intake pressures, the highest output power is obtained when the crank speed reaches 500 rpm, which also provides the maximum output torque. Finally, higher energy utilization efficiency can be obtained at the lower speed, intake pressure, and valve duration angle. This research can refer to the design of the camless valve of compressed air engine.

Research of Riveting Structure Identification and Characteristic Parameter Analysis Based on SVM

10.4028/www.scientific.net/amr.1049-1050.1554 ◽

2014 ◽

Vol 1049-1050 ◽

pp. 1554-1557

Author(s):

Jian Feng Yang ◽

Gang Jiang ◽

Jian Fei Chen

Keyword(s):

Mathematical Model ◽

Image Processing ◽

Research Result ◽

Characteristic Parameter ◽

Parameter Analysis ◽

Structure Identification ◽

Support Vector ◽

Vector Machines ◽

Set Up ◽

In order to help department to make a decision whether the equipment need maintenance, some people trained the sample of characteristic parameter for riveting structure, and set up the model to recognize target by computer vision. However, we are difficult to find the research result about the affiliation between the characteristic parameter of the riveting structure and the model. In this paper, we make the image processing first, and use SVM (Support Vector Machines) algorithm to train the sample of characteristic parameter for rivet head. Finally, we research the affiliation between the characteristic parameter for the rivet head and the mathematical model, and test the accuracy of the model.

Herald of the Bauman Moscow State Technical University Series Instrument Engineering ◽

Symmetric Control Systems

10.18698/0236-3933-2021-2-37-51 ◽

2021 ◽

pp. 37-51

Author(s):

A.I. Diveev ◽

E.A. Sofronova

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Control Systems ◽

Control Object ◽

Terminal State ◽

Initial State ◽

Phase Constraints ◽

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object