Course detail

Analytical Mechanics and Mechanics of Continuum

FSI-9AMKAcad. year: 2024/2025

The subject consists of tree significantly stand-alone parts.
The first part - Analytical mechanics - describes the mechanical system from the point of variation principles. From them the equations of motion are derived. The mutual equivalence of principles and their equivalence to Newton´s laws are proved.
The second part deals with tensors. It comes out from vector and vector components definition. The calculus rules and some special tensors are defined. The close connection between second order tensors and matrices is presented.
The third part - Mechanics of continuum - consist of classical theory of elasticity and hydromechanics with derivation of basic motion equations. The spreading of tension waves in elastic medium and change of their energy are described. The origin of shock wave in liquid and resultant changes of medium is explained. The attention is paid also to transmission processes in liquid and plain tasks solution.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

prof. RNDr. Pavel Šandera, CSc.

Department

Institute of Physical Engineering (ÚFI)

Entry knowledge

Basic knowledge of differential calculus, functions of many variables or complex variable functions.

Rules for evaluation and completion of the course

The exam has a written and an oral part.
Attendance at lectures is not compulsory, but is recommended.

Aims

Analytical mechanics creates an apposite base both the mutual binding bodies system motion solution and understanding the structure of statistic and quantum physics.
The main objective of the mechanics of continuum is to demonstrate the different progress of medium description in comparison with analytical mechanics. In mechanics of continuum we come out from concept of field of proper vector and from the analysis of that field we derive the physical processes and the results of these processes.
In analytical mechanics the students will have a clear idea of practical application of second order Lagarange´s equations for solution of system bodies motion under different type of bonds.
In mechanics of continuum, on the base of theoretical knowledge, they will be cognizant of estimation the shape of tension or flux field and analyse the possibility of critical states generation inside these fields.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

G. T. Mase, G. E. Mase: Continuum Mechanics for Engineers (Second ed.). CRC Press 1999 (EN)
J. Horský: Mechanika ve fyzice. Academia, Praha 2001. (CS)
K. R. Symon: Mechanics (Third ed.), Addison Wesley, Reading, 1971. (EN)
M. Brdička, A. Hladík: Teoretická mechanika. Academia, Praha 1987. (CS)
S. P. Timoschenko, J. Goodier.: Theory of Elasticity (Third ed.). McGraw-Hill, New York 1970. (EN)
S.P. Timoschenko, J. Gudier.: Teorija uprugosti. Překlad . Nauka, Moskva 1975. (CS)
W. Kaufmann: Technische Hydro-und Aeromechanik. Springer-Verlag Berlin/Goettingen/Heidelberg 1958. (DE)

Recommended reading

A. Bertram: Elasticity and Plasticity of Large Deformations - An Introduction (Third ed.). Springer 2012 (EN)
H. Goldstein, C. P. Poole, J. L. Safko: Classical Mechanics, Addison Wesley, San Francisco, 2011. (EN)
L. Meyrovitch: Analytical Methods in Engineering. New York: Mc.Graw-Hill, 1978. (EN)
M. Brdička, L. Samek, B. Sopko: Mechanika kontinua. Academia, Praha 2000. (CS)
M. Macur: Úvod do analytické mechaniky a mechaniky kontinua, díl I. a II. VUT v Brně 1995, 1996. (CS)
S. S. Bhavikatti: Mechanics of Solids, New Age Int. 2010 (EN)
V. Trkal: Mechanika hmotných bodů a tuhého tělesa. Nakladatelství ČSAV, Praha 1956. (CS)

Classification of course in study plans

  • Programme D-APM-P Doctoral 1 year of study, summer semester, recommended course
  • Programme D-ENE-P Doctoral 1 year of study, summer semester, recommended course
  • Programme D-IME-P Doctoral 1 year of study, summer semester, recommended course
  • Programme D-APM-K Doctoral 1 year of study, summer semester, recommended course
  • Programme D-ENE-K Doctoral 1 year of study, summer semester, recommended course
  • Programme D-IME-K Doctoral 1 year of study, summer semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

prof. RNDr. Pavel Šandera, CSc.

Syllabus

Analytical mechanics: Principle of virtual work, d´Alembert´s principle, Lagarange´s equations of second order, the other differential principles. Hamilton´s principle, Hamilton´s function, Hamilton´s canonical equation.
Tensors: Definition of tensor, operations with tensors, isotropic tensors, the second order symmetric tensor, quadric, principal axes of tensor. Characteristics of tensors from point of matrix theory.
Mechanics of continuum: Tensor of tension, tensor of deformation, generalized Hook´s low, elastic body energy, spreading and reflection of tension waves. Basic theorems of liquid kinematics, hydrostatics, basic theorems of liquid dynamics, shock wave in liquid and the origin of discontinuousness. Plane tasks, fluxional function velocity potential, complex potential, and description of plain flux field.