scholarly journals Formulation and study of the problem of optimal excitation of plate oscillations

2019 ◽  
pp. 62-65
Author(s):  
G. M. Zrazhevsky ◽  
V. F. Zrazhevska
Keyword(s):  
Objective Function ◽  
Sufficient Conditions ◽  
Analytical Determination ◽  
Main Task ◽  
Hermitian Forms ◽  
Complete Study ◽  
Concentric Circles ◽  
The Green Function ◽  
The Given

A model problem of harmonic oscillations of a hinged plate, that is is under the influence of a certain number of point concentrated forces, is considered. The plate model is considered to satisfy Kirchhoff's conditions. The main task of the consideration is to determine the optimal characteristics of excitation - the number of forces, coordinates of their application, amplitudes and phases. The optimality criterion is constructed as the standard deviation of the complex deflections from a given profile function. With the given excitation characteristics, the problem of determining the vibrations is solved in the form of a superposition of the Green functions with singularities at the points of application of forces. The Green function is constructed as a Fourier series by a circular coordinate. By using Parseval equality in L2, the objective function of the optimization problem is represented as a combination of linear and Hermitian forms with respect to complex amplitudes of forces whose matrices are nonlinear (and not convex) dependent on the coordinates of singular points. A complete study of the objective function is performed. Sufficient conditions are determined for reducing the dimension of the control space by analytical determination of the amplitudes of forces. Expressions were obtained to calculate the gradients of the objective function by angular and radial coordinates. A partial case of grouping of excitation forces on concentric circles is considered, that leads to the degeneration of the problem.

scholarly journals Some Connections between Classical and Nonclassical Symmetries of a Partial Differential Equation and Their Applications

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 524
Author(s):  
Chaolu Temuer ◽  
Laga Tong ◽  
George Bluman
Keyword(s):  
Sufficient Conditions ◽  
Partial Differential ◽  
Burgers Equations ◽  
Classical Symmetry ◽  
Nonclassical Symmetry ◽  
Kdv Type Equations ◽  
Nonclassical Symmetries ◽  
The Given

Essential connections between the classical symmetry and nonclassical symmetry of a partial differential equations (PDEs) are established. Through these connections, the sufficient conditions for the nonclassical symmetry of PDEs can be derived directly from the inconsistent conditions of the system determining equations of the classical symmetry of the PDE. Based on the connections, a new algorithm for determining the nonclassical symmetry of a PDEs is proposed. The algorithm make the determination of the nonclassical symmetry easier by adding compatibility extra equations obtained from system of determining equations of the classical symmetry to the system of determining equations of the nonclassical symmetry of the PDE. The findings of this study not only give an alternative method to determine the nonclassical symmetry of a PDE, but also can help for better understanding of the essential connections between classical and nonclassical symmetries of a PDE. Concurrently, the results obtained here enhance the efficiency of the existing algorithms for determining the nonclassical symmetry of a PDE. As applications of the given algorithm, a nonclassical symmetry classification of a class of generalized Burgers equations and the nonclassical symmetries of a KdV-type equations are given within a relatively easier way and some new nonclassical symmetries have been found for the Burgers equations.

scholarly journals Determination of the angles of pressure in the system of limitation by optimisation of linkages

Transport ◽  
2006 ◽  
Vol 21 (4) ◽  
Author(s):  
Alexandra Demokritova ◽  
Vladimir Demokritov
Keyword(s):  
Power Analysis ◽  
Analytical Determination ◽  
Straight Lines ◽  
Four Bar Linkage ◽  
The Given

In the present paper a method of analytical determination of reactions and angles of pressure is considered with the four-bar linkage as an example. The determined sequence for the expression of acceleration of the points and angle acceleration of the links is presented. Further the power analysis for Assur’s group is made. The equations of normal components of reactions are expressed as straight lines passing across given point in the given direction. The equations of the full reactions in the hinges are expressed as straight lines passing across two given points. After that the angles of pressure are expressed as the angles between directions of the speed and reactions.

The Role and Place of Budget Procedure in the System

2003 ◽  
pp. 42-49 ◽  
Author(s):  
E. Bushmin
Keyword(s):  
Budget Process ◽  
Public Expenditures ◽  
Principal Role ◽  
Process Trends ◽  
The Given ◽  
Rules Of The Game

The article is devoted to the analysis of improving budget process trends. The author offers the concept of "financial technologism". Its usage should promote an essential improvement of the budget process. The given concept is based on the fact that the regulation of budget procedure is the process of determination of "rules of the game", and the order of interaction of different institutions within the framework of the budget process, and the trends and volumes of expenses are the strategy of institutions. The procedure within the budget process plays a principal role as compared with the trends and volumes of public expenditures.

The New Swedish Cyprus Expedition 2010. Excavations at Dromolaxia Vizatzia/Hala Sultan Tekke. Preliminary results

2011 ◽  
Vol 4 ◽  
pp. 69-98 ◽  
Author(s):  
Peter M. Fischer ◽  
Patrik Klingborg ◽  
Fanny Kärfve ◽  
Fredrika Kärfve ◽  
C. Hagberg ◽  
...  
Keyword(s):  
Ground Penetrating Radar ◽  
Main Task ◽  
Phase 2 ◽  
The North ◽  
12Th Century ◽  
Area 6 ◽  
Recent Phase ◽  
The Rich ◽  
Ground Penetrating

Determination of the complete occupational sequence of the site, including investigation of pre-12th century levels which were thoroughly studied by P. Åström since the 1970s, is the main task of the planned project. During the course of the expedition (NSCE11) in spring 2010 a ground-penetrating radar survey (GPR) was carried out at Dromolaxia Vizatzia/Hala Sultan Tekke in Area 6, leading to the discovery of a large Late Cypriote complex. The compound is bordered to the north by a substantial wall, against which nine rooms (so far) could be exposed. Two occupational phases have been verified but there are indications of a third. The suggested functions of the various structures of the most recent phase are: living, working, storage and administration spaces. The rich find contexts point to the production of textiles and metal objects, and the locally produced pottery is generally of a high quality. There are also many imports, mainly from the Mycenaean sphere of culture. The locally produced vessels from Phase 2 include the “Creature krater” which is a masterpiece of a high artistic standard. Another piece of elevated artistry is the piece of a “Warrior vase”.

MODIFIKASI MODEL PEMBELAJARAN TEAM ASSISTED INDIVIDUALIZATION DENGAN STRATEGI PEMBELAJARAN TUGAS DAN PAKSA

2019 ◽  
Vol 2 ◽  
Author(s):  
Lea Christy Restu Kinasih ◽  
Dewi Fatimah ◽  
Veranica Julianti
Keyword(s):  
Cooperative Learning ◽  
Learning Strategies ◽  
Learning Process ◽  
Learning Model ◽  
Learning Models ◽  
Classroom Learning ◽  
Quality Of Learning ◽  
The Given

The selection and determination of appropriate learning strategies can improve the results to be obtained from the application of classroom learning models. This writing aims to discipline students to develop individual abilities of students to be more active in the learning process and improve the quality of learning. The learning process in Indonesia in general only uses conventional learning models that make students passive and undeveloped. In order for the quality of learning to increase, the Team Assisted Individualization learning model is combined with the task learning and forced strategies. The Team Assisted Individualization cooperative learning model is one of the cooperative learning models that combines learning individually and in groups. Meanwhile, task and forced learning strategies are strategies that focus on giving assignments that require students to complete them on time so that the learning process can run effectively. Students are required to do assignments according to the given deadline. This makes students become familiar with the tasks given by the teacher. Combining or modifying the learning model of the assisted individualization team with forced and forced learning strategies is expected to be able to make students more active, disciplined, independent, creative in learning and responsible for the tasks assigned. Therefore this method of incorporation is very necessary in the learning process and can be applied to improve the quality of learning in schools.

Sign in / Sign up

Export Citation Format

Share Document