Applied mechanics. Theoretical mechanics or applied mechanics, which one is native to the technology of recording information? Applied mechanics who to work with

The meeting of freshmen will take place on June 30 at 13:00 at the address: Volokolamskoye Highway, 4, Main Academic Building, room. 460B

Friends! We are glad to welcome you to our Institute!

Graduates of our Institute work at many aerospace enterprises in Russia.

The Institute of General Engineering Training (Institute No. 9) provides training in three areasbachelor's degree:

12.03.04 “Biotechnical systems and technologies”;
15.03.03 "Applied mechanics";
24.03.04 "Aircraft manufacturing".

One specialties:

24.05.01 “Design, production and operation of rockets and rocket-space complexes.”

And also by directionsmaster's degree:

15.04.03 "Applied mechanics";
24.04.03 "Aircraft manufacturing".

Training is carried out according to the following profiles preparation ( bachelor's degree, duration of study - 4 years ):

12.03.04 "Engineering in biomedical practice"(department No. 903);
15.03.03 “Dynamics, strength of machines and structures” (department No. 906);
15.03.03
24.03.04 “Computer engineering (CAE technologies) in aircraft manufacturing” (department No. 910B);

Specializations (specialty, duration of study - 5.5 years ):

24.05.01 “Design of structures and systems of radio engineering information complexes” (department No. 909B) - targeted training(PJSC "Radiophysics");

Programs (master's degree, duration of study - 2 years ):

15.04.03 “Mathematical modeling in the dynamics and strength of structures” (department No. 902);
24.04.04 “Aviation materials and technologies in medicine” (department No. 912B);

Antenna-feeder systems

Training of specialists in the field of “Design of structures and systems of radio engineering information complexes” has been carried out in the country since 1975 only at department 909B. Training is conducted according to the “physics and technology system”, which has the highest authority in Russia and abroad. Department 909B is based together with MIPT at the JSC Radiophysics enterprise (Planernaya metro station). It is the leader in antenna manufacturing and cooperates with foreign companies. Leading specialists of Radiophysics are involved in the educational process.

Students receive special training in the areas of:

engineering problems of strength, heat transfer, radio engineering, aerodynamics, etc.;
computer use and programming;
design of antenna systems and their mechanisms;
the latest materials, including nanotechnologies and their testing;
design of radio engineering intelligent systems.

Dynamics and strength

Departments 902 and 906 train highly qualified research engineers with a wide profile who are capable of solving complex problems using modern methods that arise in calculations and strength tests of technical systems, aviation and space technology objects.

The training process uses a new principle of training specialists, which allows you to obtain:

modern computer education based on continuous learning and independent work on modern PCs;
enhanced mathematical training combined with general engineering knowledge;
the opportunity to expand their knowledge in the process of students’ research work under the guidance of highly qualified teachers;
the opportunity to expand economic knowledge through elective training.

The training received makes it possible to successfully work not only in various areas of the aerospace industry, but also in other sectors of the economy. Specialists in this field are trained only in a few universities in the CIS and around the world.

Engineers in medicine

The medical industry needs highly qualified specialists who combine advanced research methods, technologies and materials with a fairly complete knowledge of human anatomy and biology, biomechanics, and biochemistry. Students receive training in physics and mathematics, computer technology, and a foreign language. Special disciplines are studied both at the departments of the institute and at large scientific and medical centers. Extensive and deep knowledge in the field of high technologies, materials, and related fields of medicine will provide a specialist with the opportunity to successfully work in enterprises of various profiles.

Nanotechnology in aircraft manufacturing

Department 910B is the base department of the Institute of Applied Mechanics of the Russian Academy of Sciences (IPRIM RAS).

In the learning process, the principle of harmonious combination of fundamental and engineering education is implemented, which allows the graduate to:

receive enhanced mathematical training combined with general engineering knowledge;
acquire modern computer education based on continuous learning and independent work on the latest computer equipment;
expand your knowledge beyond the mandatory program by including research work in the curriculum under the guidance of highly qualified specialists using the scientific and experimental equipment of IPRIM RAS.

Computer engineering allows you to create detailed computer models of complex machines and mechanisms, conducting their in-depth analysis taking into account real operating conditions.

Lecture notes

in the course "Applied mechanics"

Section I Theoretical mechanics

Topic 1. Introduction. Basic Concepts

Basic concepts and definitions

Mechanics is a field of science whose purpose is to study the motion and stress state of machine elements, building structures, continuous media, etc. under the influence of applied forces.

In theoretical mechanics, general laws of the objects under study are established without connection with their specific applications. Theoretical mechanics is the science of the most general laws of motion and equilibrium of material bodies. Movement, understood in the broadest sense of the word, covers all phenomena occurring in the world - the movement of bodies in space, thermal and chemical processes, consciousness and thinking. Theoretical mechanics studies the simplest form of motion - mechanical motion. Because the state of equilibrium is a special case of mechanical motion, then the task of theoretical mechanics also includes the study of the equilibrium of material bodies. Theoretical mechanics is the scientific basis of a number of engineering disciplines - strength of materials, theory of mechanisms and machines, statics and dynamics of structures, structural mechanics, machine parts, etc.

Theoretical mechanics consists of 3 sections - statics, kinematics and dynamics.

Statics is the study of forces. Statics examines the general properties of forces and the laws of their addition, as well as the conditions of equilibrium of various systems of forces. 2 main problems of statics: 1) the problem of reducing a system of forces to its simplest form; 2) the problem of equilibrium of a system of forces, i.e. the conditions under which this system will be balanced are determined.

Kinematics is the study of the movement of material bodies from the geometric side, regardless of the physical causes causing the movement.

Dynamics is the study of the movement of material bodies under the influence of applied forces.

In its structure, theoretical mechanics resembles geometry - it is based on definitions, axioms and theorems.

A material point is a body whose dimensions can be neglected under the given conditions of the problem. Such a body is called an absolutely rigid body. In which the distance between any of its points remains constant. In other words, an absolutely rigid body retains its geometric shape unchanged (does not deform). A rigid body is called free if it can be moved from a given position to any other. A rigid body is called non-free if its movement is impeded by other bodies.

Force is the action of one body on another, expressed in the form of pressure, attraction or repulsion. Force is a measure of the mechanical interaction of bodies, determining the intensity of this interaction. Force is a vector quantity. It is characterized by the point of application, the line of action, the direction along the line of action and its magnitude or numerical value (module).

For force we have (Figure 1.1): A– point of application, ab– line of action; direction of force along this line from A To IN(indicated by an arrow), is the magnitude (modulus) of the force.

Forces are represented by letters, etc. with dashes on top. The magnitudes of these forces are depicted in the same letters, but without dashes - F, P, Q etc. Dimension: .

The set of forces applied to a body is called a system of forces. The system of forces can be flat and spatial. A system of forces is convergent if the lines of action of all forces intersect at one point (Figure 1.2).

Two systems of forces are called equivalent if they have the same effect on all points of the body.

If, under the influence of a system of forces, a rigid body remains at rest, then this state of the body is called a state of equilibrium, and the applied system of forces is called balanced. A balanced system of forces is also called statically equivalent to zero.

The force equivalent to a given system of forces is called the resultant force.

Forces acting on a body from other bodies are called external forces. The forces of interaction between particles of a body are called internal forces.

A force applied to a body at any one point is called a concentrated force. Forces acting on all points of a given volume, surface or line are called distributed forces.

A balancing force is a force equal in magnitude to the resultant force, but directed in the opposite direction (Figure 1.3).

1.2. Axioms of statics

Statics is based on several axioms or propositions, confirmed by experience and therefore accepted without proof.

Axiom 1. On the equilibrium of two forces applied to a rigid body.

For the equilibrium of two forces applied to a solid body, it is necessary and sufficient that these forces be opposite and have a common line of action (Figure 1.4)

The action of a balanced system of forces on a rigid body at rest does not change the rest of this body.

Axiom 2. About joining or rejecting a balanced system of forces.

Without changing the action of a given system of forces, you can add to or subtract from this system any balanced system of forces (Figure 1.5).

Axiom 3. Parallelogram law.

The magnitude of the resultant force and its direction are determined accordingly by the cosine theorem, i.e. the resultant of two forces coming from one point comes from the same point and is equal to the diagonal of a parallelogram constructed on these vectors (Figure 1.6)

– analytical solution,

Geometric solution:

Where – scale factor, N/mm.

Axiom 4. On the equality of action and reaction forces.

The forces with which two bodies act on each other are equally opposite and have a common line of action (Figure 1.7.)

The forces of action and reaction do not form a balanced system of forces, because they are applied to different bodies.

After graduating from the university with a degree in applied mechanics, a student will be able to work as an engineer in various fields, a computer specialist, an applied mechanics specialist, and a tribologist.
A bachelor's degree opens up opportunities to connect your life with the latest developments in physical, mechanical and computerized problems. The graduate will be able to take part in computational and experimental research, work with applied problems and find new ways to solve them.
The qualification level will allow you to create professional reports, presentations, scientific reports on research and knowledge in the field of applied mechanics. The graduate will be able to independently design machines with a high level of wear resistance, which will meet quality standards and will be relevant in the market.
The bachelor moves to a new level of designing parts and mechanisms through computerized control systems. His competence also includes expanding the design and engineering base of the applied mechanics industry.

What are they studying?

Federal Agency for Education

Russian Chemical-Technological University named after. DI. Mendeleev

APPLIED MECHANICS

Approved by the University Editorial Board as a teaching aid

Moscow 2004

UDC 539.3 BBK 34.44; -04*3.2);30/33*3.1):35 P75

Reviewers:

Doctor of Physical and Mathematical Sciences, Professor of the Russian Chemical Technology University. DI. Mendeleev

V.M. Aristov

Doctor of Technical Sciences, Professor of the Russian Chemical Technology University. DI. Mendeleev

V.S. Osipchik

Candidate of Technical Sciences, Associate Professor, Moscow State University of Environmental Engineering

V.N. Frolov

Applied mechanics/ S.I. Antonov, S.A. Kunavin,

P75 E.S. Sokolov Borodkin, V.F. Khvostov, V.N. Chechko, O.F. Shlensky, N.B Shcherbak. M.: RKhTU im. DI. Men-

Deleeva, 2004. 184 p. ISBN 5 – 7237 – 0469 – 9

The general principles for performing strength calculations of elements of the main structures of chemical equipment are given. Contains information necessary to complete homework in the applied mechanics course.

The manual is intended for full-time, part-time and evening students.

UDC 539.3 BBK 34.44; -04*3.2);30/33*3.1):35

INTRODUCTION

Progress in chemical technology cannot be imagined without the development of chemical engineering, which is based on the laws of mechanics. The laws and mathematical models of mechanics make it possible to evaluate the capabilities of operating and newly designed equipment of any chemical production, be it the production of silicate and polymer materials and products, gunpowder or quantum electronics materials.

A chemical technologist must know and understand the laws of mechanics enough to conduct a business conversation in the same language with a mechanical engineer engaged in direct design, not demand the impossible from him, and in collaboration with him, look for optimal solutions, achieving the greatest efficiency of the designed equipment.

An important stage in the preparation of a chemical technologist is the formation of engineering thinking. The discipline of Applied Mechanics makes a significant contribution to this important process. The course of applied mechanics makes full use of the information obtained by students while studying general scientific and engineering disciplines such as higher mathematics, physics, computational mathematics, etc.

Applied mechanics is a complex discipline. It includes, to one degree or another, the main provisions of the courses “Theoretical Mechanics”, “Strength of Materials” and “Machine Parts”.

In the process of improving the educational process, the team of the Department of Mechanics developed an unconventional approach to the presentation of the course "Applied Mechanics": the material of the disciplines included in it (theoretical mechanics, strength of materials, machine parts)

is considered as a single whole, a unified approach to the presentation of the material is provided, and organically related sections of disciplines are combined. If possible, sections of material resistance have direct access to the corresponding sections of chemical production machine parts. Theoretical mechanics is presented only by those sections that are actively used in the study of other topics in this discipline, and are also necessary for a process engineer to understand mechanical processes in chemical technology.

The course additionally includes information about basic structural materials, pipelines, general-purpose capacitive equipment and mechanical processes of chemical technology. The course is provided with a textbook specially prepared for students taking into account the specifics of teaching “Applied Mechanics” at a chemical engineering university. However, no matter how necessary a textbook is, in connection with changing university curricula, in order to strengthen the general technical training of process engineers, teachers may introduce additional sections in the course “Applied Mechanics” and change the methodology of lecture material and seminar classes.

Thus, students should rely less on the textbook and more on classroom training, which will allow them to become not only performers, but also organizers of production at an earlier stage.

Transferring technologies developed in laboratories to the scale of industrial production, ensuring the effective use of technological equipment, participation in the development of technical specifications for the creation of new machines and devices, mechanical testing of new materials - all this presupposes the presence of solid knowledge in the field of mechanics among chemical technologists.

A process engineer who has studied mechanics most sensitively senses the peculiarities of the technological process and can set the optimal design of the device or apparatus being designed, which ultimately determines the productivity and quality of the manufactured product. For example, correctly calculated temperature fields of the walls and the design of the working chamber of a plasma-chemical reactor made of heat-resistant materials created in accordance with these and mechanical calculations can increase the productivity of the reactor several times.

Chemists have known for a long time that diamond and graphite have the same composition, as well as the possibility of their mutual transformation. But only the joint efforts of mechanical and process engineers and the latest advances in the creation of special pressing equipment made it possible to turn ordinary graphite into artificial diamonds.

In conclusion, you should add information about the academic mobility of both the student and the certified specialist, in other words, about the possibility of changing your specialty for certain reasons or the possibility of studying in a different profile. Mechanics and, in particular, applied mechanics form the basis for the training of specialists in many other specialties. Therefore, the study of mechanics will allow a graduate of the Russian Chemical Technical University named after. D.I. Mendeleev to work in other areas of technology and successfully improve their skills.

LIST OF SYMBOLS

R, F - force vectors, N.

Fx ,Fy , Fz , Rx , Ry , Rz , Qx , Qy , Qz , - projections of force on the axis x, y, z, N. i, j, k - unit vectors.

M o (F) - vector of the moment of force F relative to the center O,.Hm. σ, τ - normal, tangential stress, Pa.

ε, γ - linear, angular deformation, radian. σ x, σ y, σ z - projections of stresses on the x, y, z axes. ε x, ε y, ε z - projections of deformations on the x, y, z axes.

∆l, ∆ a - absolute deformations of segments l and a, m.

E - elastic modulus of the first row (Young's modulus), Pa. G - elastic modulus of the second row (shear modulus), Pa.

µ - transverse contraction ratio (Poisson), dimensionless. A - cross-sectional area, m2 [σ], [τ] - permissible normal and tangential stress, Pa U - potential energy, N.m

W - work of force, Nm

u - specific potential energy, Nm/m3

σ in - tensile strength, temporary resistance, Pa σ t - yield strength, Pa.

σ y - elastic limit, Pa.

σ pc - proportionality limit, Pa. ψ - relative residual narrowing. δ - relative residual elongation. n - safety factor, Pa.

S x, S y - static moments about the x, y, m3 axes. J x, J y - moments of inertia about the x, y, m4 axes. J p - polar moment of inertia, m4.

φ - twist angle, rad.

θ - linear relative twist angle, rad/m.

[θ] - permissible relative angle of twist, rad/m. W p - polar moment of resistance, m3.

q - intensity of distributed load, N/m. ρ - radius of curvature of the elastic line, m.

W x - axial moment of resistance, mz. σ 1, σ 2, σ 3 - main stress, Pa.

σ eq - equivalent stress, Pa.

τ max - maximum shear stress, Pa. P cr - critical force, N.

µ pr - length reduction coefficient. i - radius of gyration, m.

λ - flexibility, dimensionless.

K - dynamic coefficient. ω - rotation frequency, s-1.

σ a, σ m - amplitude and average cycle stress, Pa.

σ max, σ min – maximum and minimum cycle stress, Pa.

σ -1 - fatigue strength limit under a symmetric loading cycle (fatigue limit), MPa..

n σ n τ - fatigue strength safety factor for normal and tangential stresses, Pa.

g - acceleration of the forces of gravity, m/s2. F st – static deflection, m.

β is the ratio of the mass of the rod to the mass of the falling load, dimensionless. δ 11 - displacement caused by a unit force in the direction of action

unit force, m/N.

Ω – frequency of forced oscillations, s-1.

1. STATICS OF A SOLID BODY

1.1. Basic Concepts

Statics is the branch of mechanics that studies the relative equilibrium of material bodies under the influence of forces applied to them. Abstract bodies are considered, for which the physical structure and chemical properties do not matter. Bodies are assumed to be absolutely solid, i.e. do not change their shape and size under load and are not susceptible to destruction. The distances between any two points in such bodies remain unchanged.

The main task of statics is to determine the forces acting on the structural elements of machines and devices.

Force is a quantitative measure of the mechanical interaction of bodies. Force is a vector quantity and can be projected onto the coordinate axes x, y (Fig. 1.1) and presented as:

F = Fx i + Fy G j + Fz k ,

where i, j, k are unit vectors. Force module

F = (F x )2 + (F y )2 + (F z )2 ,

where: F x , F y , F z – projections of force F onto the coordinate axes. The force dimension is newton [H].

If the system of forces does not cause a change in the kinematic state of the body (its movement), the body is said to be in a state

static equilibrium (or rest), and the applied system of forces is balanced.

A force whose mechanical action is equivalent to a given system of forces is called resultant. The force that complements a given system to equilibrium is called balancing.

1.2. Axioms of statics

1. A free body is in equilibrium under the action of two forces only if these forces are equal in magnitude, act in one straight line and are directed in opposite directions. An obvious consequence: force alone does not ensure the balance of the body.

2. The balance of the body will not be disturbed if a balanced system of forces is added to it or taken away.

Corollary: force is a sliding vector, i.e. can be transferred to any point along the line of its action.

3. The resultant of two converging forces is the diagonal of a parallelogram constructed on these forces as on the sides (Fig. 1.2).

4. Bodies interact with each other with forces equal and oppositely directed.

1.3. The concept of moment of force

IN In cases where a force creates a turning effect on a body, we speak of a moment of force. The measure of such impact is the moment of force. The moment of force F relative to the center O (Fig. 1.3.) is a vector product

Μ 0 (F) = r x FG .

Modulus of this vector

Μ 0 (F) = F r sin α = F h,

where h is the arm of the force F relative to the center O, equal to the length of the perpendicular lowered from the center to the line of action of the force, r is the radius vector of the point of application of the force (Fig. 1.3). Moment dimension [N m]. Vector M 0 (F) acts perpendicular to the plane passing through the line of action of the force and the center 0. Its direction is determined by the rule "bu-

Symbolic language of the Slavs

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