Course name:
Course code:
Number of contact hours/week:
Physics
KFY/TFY
4 (lecture) + 1 (laboratory work) + 1 (seminar)
2 (self-study)
Course guarantor:
RNDr. Radomír Kuchta
Requirements for the successful completion of the course:
Continuous assessment:
fulfilment of test requirements
Final assessment:
combined examination (written and oral)
Only those who have successfully met the continuous assessment requirements will be
permitted to take the examination.
Topics of lectures according to weeks:
1.
Introduction, scalars and vectors, velocity and acceleration, projectile motion,
circulation motion
2.
Linear momentum, Newton's law, kinetic energy, potential energy, elastic and inelastic
collisions, motion in the gravitational field, angular momentum, combined rotation and
translation
3.
Postulates of relativity, length contraction and time dilatation, the mass-energy relation
4.
Linear harmonic oscillator, damped and forced vibrations, modulation, characteristic
frequencies and modes of vibration
5.
Waves and their propagation, superposition of waves, interference and diffraction,
stationary waves, the Doppler effect
6.
Characteristics of materials, Hooke's law, pressure in liquids, viscosity, laminar and
turbulent flows, thermal energy and its transfer
7.
Typical processes in gases, entropy, laws of thermodynamics, heat engines
8.
Electric field and its characteristics, electric current, power and electrical heating
9.
The origin of a magnetic field, torque on a current loop, electromagnetic induction and
Faraday's law, energy stored in the electromagnetic field, alternating currents
10.
Electromagnetic waves, visible light and consequences of its wave nature, reflection
and refraction of light, optical devices
11.
Radiation of a blackbody, photoelectric effect, the Compton effect, quantum nature of
light, photons and their properties
12.
Particles as wave packets, the uncertainty principle, structure of the hydrogen atom,
LASER
13.
Energy of an atomic nucleus, nuclear fission and fusion, fundamental particles and
forces, quantum computer
Topics of laboratory work and seminars according to weeks:
1.-13. Presentation of examples and solution of problems concerning the topics dealt with in
the lectures alternate with laboratory work.
List of literature:
[1]
Bueche, F.J.: Principles of Physics, McGraw-Hill, New York 1988,
ISBN 0-07-100150-6
[2]
Beiser, A.: Concepts of Modern Physics, McGraw-Hill, New York 1987,
ISBN 0-07-004473-2
Course name:
Application of Cybernetics to Mechanical Engineering
Course code:
KKY/AKS
Number of contact hours/week: 2 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Doc. Ing. Eduard Janeček, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
fulfilment of test requirements
Final assessment:
combined examination (written and oral)
Topics of lectures according to weeks:
1. Cybernetic systems (CS), information in CS
2. Linear dynamic systems (LDS) – internal and external system description
3. Frequency domain description, frequency characteristics and time responses of LDS
4. Computer models of LDS
5. Stability of LDS
6. Automatic regulation and compensation; transfer functions in control loops; stability and
quality of control loops; Nyquist criterion
7. PID, PSD regulators, setting of parameters
8. Cybernetic systems with two-state variables
9. Programmable logic controllers, IEC 1131-3 programming standard
10. Sensors in automatic control systems
11. Actuators in automatic control systems
12. Industrial communication in automatic control systems
13. Control system structure for process and machine control
Topics of seminars according to weeks:
1.- 3. Introduction to software for design and simulation; experiments with cybernetic
systems
4. – 7. Measurement of static and dynamic characteristics of cybernetic systems – laboratory
report
8.– 11. Design of controllers, model and real-time implementations, simulation experiments –
laboratory report
12 - 13. Logical control; design of programmable logic controllers, model and real-time
implementations, simulation experiments – laboratory report
List of literature:
[1]
Goodwin G.C.: Control System Design, Prentice Hall , 2001
[2]
Weinmann A.: Regelungen, Springer-Verlag , Wien 1987
Course name:
Course code:
Number of contact hours/week:
Geometry
KMA/GE
4 (lecture) + 2 (seminar)
3 (self-study)
Course guarantor:
Doc. RNDr. František Ježek, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments and
fulfilment of test requirements
Final assessment:
combined examination (oral and written)
Only those who have successfully met the continuous assessment requirements will be
permitted to take the examination.
Topics of lectures according to weeks:
1.
Projections (linear perspective, axonometry, orthographic projection)
2.
Monge projection (topological and metrical problems)
3.
Polynomials, fundamental theorem of algebra; matrix algebra
4.
Matrices; determinants
5.
Linear systems, Frobenius theorem, Gauss elimination
6.
Axonometry, Pohlke theorem, realistic visualization
7.
Vector algebra; analytic geometry in the space
8.
Analytic geometry in the space (linear objects)
9.
Geometry of curves and surfaces
10.
Rotational and helical surfaces
11.
Envelope and developable surfaces
12.
Geometric transformation; homogeneous coordinates
13.
Quadrics (classification)
Topics of seminars according to weeks:
1.
Conic sections; Pascal theorem
2.
Monge projection (topological problems)
3.
Monge projection (metrical problems)
4.
Polynomials; matrix algebra
5.
Matrices; determinants
6.
Linear systems, Gauss elimination
7.
Axonometry
8.
Analytic geometry in the space (linear objects)
9.
Curves, helix
10.
Elementary surfaces (cylinder, cone), section
11.
Rotational and helical surfaces
12.
Envelope and developable surfaces
13.
Transformations, matrix form, homogeneous coordinates
List of literature:
[1] Kargerová M.: Geometry and Computer Graphics, ČVUT Praha, 1998.
[2] Berger M.: Geometry I, II, Springer 1994, 1996.
Course name:
Course code:
Number of contact hours/week:
Geometric and Computational Modelling
KMA/GPM
3 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Doc. RNDr. František Ježek, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
combined examination (oral and written)
Only those who have successfully met the continuous assessment requirements will be
permitted to take the examination.
Topics of lectures according to weeks:
1. Matrix form of 3D transformation and projections; homogeneous coordinates
2. Curves and surfaces, parametric representation, curvature and Frenet frame
3. Spline curves, spline under tension
4. Bézier curves, the Bernstein basis and its properties (de Casteljau algorithm, convex hull,
variation diminishing property), spline representation
5. B-spline basis, properties of B-spline curves (Cox - de Boor algorithm)
6. Rational curves; NURBS - description of conic sections
7. Differential geometry of surfaces (Gauss and main curvatures)
8. Biparametric surfaces, patches; Bézier, B-spline and NURBS surfaces
9. Triangular patches - barycentric coordinates
10. Coons patches (bilinear, bicubic, blending, lofting)
11. Geometrical modelling in CAD, B - and CSG representation, features based modelling
12. Topology, variational geometry, dimension driven shape modification
13. New trends in CAGD
Topics of seminars according to weeks:
1. Analytical geometry, vector algebra, conic sections, quadrics
2. Matrix form of transformation in 3D, homogeneous coordinates
3. Differential geometry of curves
4. Laboratory work (spline modelling in Matlab, motion animations)
5. Bézier curves
6. B-spline and NURBS
7. Laboratory work (free form modelling)
8. Laboratory work (NURBS modelling)
9. Laboratory work (variational and parametric modelling)
10. Coons patches
11. Project presentation and evaluation
12. Project presentation and evaluation
List of literature:
[1] Farin, G. (Ed.): Handbook of computer aided geometric design, Elsevier 2002.
Course name:
Course code:
Number of contact hours/week:
Mathematics 3
KMA/M3
3 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Prof. RNDr. Stanislav Míka, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
fulfilment of test requirements
Final assessment:
combined examination (oral and written)
Topics of lectures according to weeks:
1.-4. Number and function sequences and series, convergence; Fourier’s series
5.-6. Laplace’s transformation (in real numbers) - use for solving ordinary differential
equations, applications
7.-8. Introduction to vector analysis; scalar and vector arrays
9.-12. Parametrization of curves and surfaces; curve and surface integrals
13.
Integral theorems of vector analysis and their applications
Topics of seminars according to weeks:
In the seminars students have an opportunity to apply the knowledge acquired in the lectures
to the solution of practical problems. The topics of the seminars are arranged in the same
chronological order as in the lectures.
List of literature:
[1]
Lovrič, M.: Vector Calculus. Addison-Wesley Publishers Limited, 1997,
ISBN 0-201-42797-4
Course name:
Course code:
Number of contact hours/week:
Mathematical Models in Econometrics
KMA/MME
2 (lecture) + 1 (seminar)
1 (self-study)
Course guarantors:
Prof. RNDr. Stanislav Míka, CSc.
Mgr. Blanka Šedivá
Requirements for the successful completion of the course:
Continuous assessment:
fulfilment of test requirements
Final assessment:
combined examination (oral and written)
Topics of lectures according to weeks:
1.-2. Introduction; the simple and multiple regression model; least-squares estimator of its
parameters, maximum-likelihood estimation, general method of moments approaches
to the estimation
3.
Heteroskedasticity, autocorrelation and multicolinearity
4.
Numerical optimization methods for estimators
5.
Probit and logit models
6.
Models of expectations
7.
Modelling of nonlinear economic relationships
8.
Modelling of simultaneous equations; identification, methods of estimation of
parameters
9.
Stochastic models for time series; AR, MA, ARMA, ARIMA models; estimate of
coefficients, autocorrelation and partial autocorrelation functions
10.
Economic time series with time-varying volatility (ARCH, GARCH models)
11.
Vector autoregression models; cointegration, Granger causality
12.
Economic dynamics, linearities in dynamic economic systems
13.
Nonlinearities in dynamic economics
Topics of seminars according to weeks:
In the seminars students have an opportunity to apply the knowledge acquired in the lectures
to the solution of practical problems. The topics of the seminars are arranged in the same
chronological order as in the lectures.
List of literature:
[1]
Judge, G. a spol.: Theory and Practice of Econometrics, Wiley and Sons, NY 1985.
Course name:
Course code:
Number of contact hours/week:
Mathematics for FST 1
KMA/MS1
4 (lecture) + 1 (seminar)
1 (self-study)
Course guarantor:
Prof. RNDr. Stanislav Míka, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
fulfilment of test requirements
Final assessment:
combined examination (oral and written)
Topics of lectures according to weeks:
1.-2. Sequences and series in R1
3.
Difference equations
4.-5. Functions of one variable
6.-8. Differential calculus
9.-11. Integral calculus
12.
Elementary differential equations
13.
Simple dynamic systems
Topics of seminars according to weeks:
1.-2. Sequences and series in R1
3.
Difference equations
4.-5. Functions of one variable
6.-8. Differential calculus
9.-11. Integral calculus
12.
Elementary differential equations
13.
Simple dynamic systems
List of literature:
[1]
Edwards, C., H.: Calculus with Analytic Geometry. Prentice Hall, New Jersey, 1998,
ISBN 0-13-736331-1
Course name:
Course code:
Number of contact hours/week:
Mathematics for FST 2
KMA/MS2
4 (lecture) + 1 (seminar)
2 (self-study)
Course guarantor:
Prof. RNDr. Stanislav Míka, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
fulfilment of test requirements
Final assessment:
combined examination (oral and written)
Topics of lectures according to weeks:
1.
Introduction; differential models of dynamic systems; ordinary differential equations
of the first order
2.
Ordinary linear differential equations of arbitrary order, n = 2,3, …
3.
Systems of ordinary linear differential equations of the first order and of the second
order
4.
Scalar functions of several variables, limit, continuity
5.
Differential calculus of real-valued functions of several variables
6.
Optimization; local and constrained local extremes of scalar functions of several
variables
7.
Integral calculus of real-valued functions of several variables; double and three-fold
integrals
8.
Curve and surface integrals
9.
Scalar fields and vector fields; vector calculus
10.
Vector functions; vector differential calculus
11.
Differential and integral characteristics of vector fields
12.
Integral theorems, integral theorems of vector fields
13.
Integrals with parameters; course evaluation
Topics of seminars according to weeks:
1.-2. Ordinary differential equations of the first order; ordinary linear differential equations
of arbitrary order, n = 2,3,…; fundamental, general and particular solutions
3.-4. Systems of ordinary linear differential equations of the first order with constant
coefficients; elimination method; scalar functions of several variables, graphs and
contour curves
5.-6. Partial derivatives; total differential; local and constrained local extremes of scalar
functions of several variables
7.-8. Double and three-fold integrals; curve and surface integrals
9.-10. Scalar fields and vector fields; gradient of a scalar field, divergence of a vector field,
curl of a vector field
11.-12. Integral theorems; Green’s theorem, transformation of double integrals into line
integrals, Gauss-Ostrogradskij’s theorem, Stokes-theorem
List of literature:
[1]
Howard A.: Calculus with Analytic Geometry. John Wiley, New York, 1995,
ISBN 0-471-59495-4
Course name:
Course code:
Number of contact hours/week:
Numerical and Geometric Modelling
KMA/NGM
2 (lecture) + 1 (seminar)
1 (self-study)
Course guarantor:
Doc. RNDr. František Ježek, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
combined examination (oral and written)
Only those who have successfully met the continuous assessment requirements will be
permitted to take the examination.
Topics of lectures according to weeks:
1.
Solution of systems of linear algebraic equations - iterative methods
2.
Interpolation and approximation
3.
Differential geometry of curves and surfaces, parameterization, curvature
4.
Spline function, curve and surface
5.
Bézier curves, B-spline
6.
NURBS modelling
7.
Coons patches
8.
Numerical solution of ordinary differential equations
9.
Numerical solution of partial differential equations
10.
Solid modelling, exchange formats in CAD
11.
Visualization and animation
12.
Variational and parametric modelling
13.
New trends in CAD/CAM, PLM (product life-cycle management)
Topics of seminars according to weeks:
1.
Analytical geometry, vector algebra, matrix description of transformation
2.
Solving of systems of linear algebraic equations - iterative methods
3.
Interpolation and approximation
4.
Differential geometry of curves and surfaces, parameterization, curvature
5.
Spline function, curve and surface
6.
Laboratory work (spline modelling in Matlab)
7.
Bézier, B-spline NURBS modelling
8.
Laboratory work (NURBS modelling in Rhino or Catia)
9.
Numerical solution of ordinary differential equations
10.
Numerical solution of partial differential equations
11.
Laboratory work (numerical modelling)
12.
Variational and parametric modelling
13.
Case studies of CAD/CAM/PLM
List of literature:
[1] Farin, G. (Ed.): Handbook of computer aided geometric design. Elsevier 2002
Course name:
Course code:
Number of contact hours/week:
Probability and Statistics B
KMA/PSB
2 (lecture) + 1 (seminar)
2 (self-study)
Course guarantor:
Doc. RNDr. Jiří Reif, CSc.
Requirements for the successful completion of the course:
Final assessment:
test
Topics of lectures according to weeks:
1.
Random events, probability and its properties
2. Conditional probability, total probability theorem; random variable, distribution function
3.
Discrete random variables – expected value and variance, binomical and Poisson
distribution
4.
Continuous random variables – probability density function, expected value and
variance, uniform, exponential and normal distributions
5.
Approximation by a normal distribution; quantiles (percentiles) of a continuous
random variable, median, quartiles
6.
Vector of random variables, covariance, correlation coefficient, two-dimensional
normal distribution
7.
Descriptive statistics, frequency tables, histograms, averages, dispersion statistics
8.
Estimation of parameters, point estimations, interval estimations, confidence level
9.
Statistical hypothesis, significance level, critical value; tests of a mean, tests of a
variance, tests comparing two parameters
10.
Goodness-of-fit tests, chi-square test, contingency tables
11.
Correlation, sample correlation coefficient and its properties, tests of a linear
relationship
12.
Regression, linear regression, coefficient of determination, multiple regression
13.
Statistical methods of quality assurance
Topics of seminars according to weeks:
1.- 2. Classical and empirical approach to probability, addition and multiplication rule,
probability of complement event
3.- 4. Use of the total probability theorem, distribution function, expected value and variance
5.- 6. Some discrete random variables, approximation of binomial distribution by a Poisson
distribution
7.- 8. Normal and exponential distributions and their applications
9.-10. Confidence intervals, chi-square test, contingency tables
11.
Correlation coefficient, tests of linear relationship
12.-13. Final test
List of literature:
[1] Farlow, S. J., Haggard, G. M.: Applied Mathematics, Random House, New York, 1988.
[2] Triola, M. F.: Elementary Statistics, The Benjamin Publishing Comp., California, 1989.
Seminar – Differential Calculus
KMA/SDP
0 (lecture) + 2 (seminar)
1 (self-study)
Course guarantor:
RNDr. Petr Tomiczek, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
written examination
Course name:
Course code:
Number of contact hours/week:
Topics of seminars according to weeks:
1.
Elements of the set theory, real numbers, supremum, infimum
2.
Sequence of real numbers, boundedness, monotony, limit of sequence
3.
Series of real numbers, partial sums, limit of series
4.
Convergence and absolute convergence of series, alternating series
5.
Real functions of one independent real variable, limits
6.
Continuity, uniform continuity of function
7.
Difference, derivative, differential of function
8.
Basic theorems of differential calculus
9.
Taylor formula and derivatives of a higher order, graphs of functions
10.
Integration, indefinite integrals, properties of integrals
11.
Integration techniques, substitution, by parts
12.
Newton integral, basic theorem of integral calculus
13.
Riemann integral
List of literature:
[1] Neustupa, J.: Mathematics I, ČVUT Praha, 1996
[2] Bubeník, F.: Problems to mathematics for engineers, Vydavatelství ČVUT, 1999
Seminar – Integral Calculus
KMA/SIP
0 (lecture) + 2 (seminar)
1 (self-study)
Course guarantor:
RNDr. Petr Tomiczek, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
written examination
Course name:
Course code:
Number of contact hours/week:
Topics of seminars according to weeks:
1.
Vector valued function, linear normed space, complex functions of one variable,
curves in Rn, Euler´s equality
2.
Differential equations, first-order equations, separation of variables, homogeneous,
nonhomogeneous equations
3.
Linear equations of the first-order and arbitrary-order, variations of parameters
4.
Boundary value problems, systems of first order equations
5.
Sequences and series of functions, power series
6.
Trigonometrical and general Fourier series; Laplace series
7.
Functions of several variables, limits and continuity
8.
Differential calculus in several variables, higher order differentials, Taylor series
9.
Implicit function theorem and solvability of functional equations
10.
Elements of the optimization theory in Rn
11.
Transformation of variables in Rn and Riemann integral in Rn
12.
Integration in R2 and R3 using the Fubini theorem and substitution methods
13.
Integrals depending on parameters
List of literature:
[1]
Bubeník, F.: Problems to mathematics for engineers, ČVUT Praha, 1999
Course name:
Course code:
Number of contact hours/week:
Experimental Mechanics
KME/EXM
2 (lecture) + 2 (seminar and laboratory work)
2 (self-study)
Course guarantor:
Prof. Ing. František Plánička, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
oral examination
Topics of lectures according to weeks:
1. Introduction; fundamentals of the theory of experiment, goal, stages, measuring methods,
experimental chains
2. Basic relations for stress and strain, Mohr’s diagram for strain; Cauchy’s equations
3. Experimental stress analysis; goals, measuring methods, methods for determining stress
and strain in bodies; mechanical, string, pneumatic and electrical resistance gauges
4. Electrical resistance gauges; basic equation, gauge design, measuring of small changes in
resistance, gauge factor; resistance gauge properties; linearity, hysteresis, relaxation,
transverse sensitivity, allowable voltage
5. Amplifiers; bridge equilibrium, gauge connection, full bridge, half bridge, single gauge;
influence of operating conditions on measurement
6. Model similitude
7. Linear systems, SISO, MIMO systems; experiment and its aim
8. Fourier transform, Dirac impulse
9. Excitation – loading, static, dynamic; vibrators – mechanical, electrical; sensors; catchers
of displacements, velocities, accelerations
10. Experimental rotor balancing
11. Experimental modal analysis
12. Intensitimetry
13. Identification; direct, indirect
Topics of seminars and laboratory work according to weeks:
14. Safety regulations, laboratory equipment
15. Basic relations of the theory of elasticity applied to experimental analysis
16. Measuring of Young´s modulus using mechanical gauges
17. Electrical resistance gauges, fixing procedure; electrical resistance gauge factor
determination
18. Experiment preparation – plane problem; experimental stress analysis of a thin cylinder
under internal pressure
19. Experimental data processing and evaluating
20. Amplitude and amplitude-frequency characteristics; experimental investigation of the
transfer function
21. FFT, correlation theory, power spectral density
22. Digital processing of ergodic processes, response of a linear system to random excitation
23. Experimental rotor balancing
24. Experimental modal analysis
25. Intensitimetry
26. Industrial visit
List of literature:
[1]
Dally, J. W., Riley, W. F.: Experimental Stress Analysis, McGraw-Hill 1991,
ISBN 0-07-015218-7
[2]
Handbook on Experimental Mechanics, VCH Publishers, 1993,
ISBN 1-56081-640-6
[3]
Ewins, D. J.: Modal Testing: Theory and Practice, Bruel&Kjær, 1986
Course name:
Course code:
Number of contact hours/week:
Experimental Stress Analysis
KME/EXP
2 (lecture) + 2 (seminar and laboratory work)
2 (self-study)
Course guarantor:
Prof. Ing. František Plánička, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
oral examination
Topics of lectures according to weeks:
1. Introduction; fundamentals of the theory of experiment, goal, stages, measuring methods,
experimental chains
2.
Basic relations for stress and strain, Mohr’s diagram for strain; Cauchy’s equations
3.
Experimental stress analysis; goals, measuring methods, methods for determining
stress and strain in bodies; mechanical, string, pneumatic and electrical resistance
gauges
4.
Electrical resistance gauges; basic equation, gauge design, measuring of small changes
in resistance, gauge factor
5.
Resistance gauge properties; linearity, hysteresis, relaxation, transverse sensitivity,
allowable voltage
6.
Amplifiers; bridge equilibrium, gauge connection, full bridge, half bridge, single
gauge
7.
Influence of operating conditions on measurement; temperature compensation, selfcompensation; cyclic loading, humidity, pressure, radiation influence; gauge types
8.
Influence of operating conditions on measurement; temperature compensation, selfcompensation; cyclic loading, humidity, pressure, radiation influence; gauge types
9.
Amplifiers for static and dynamic measurements; determining stress components from
measured strain components; single gauge, rosette
10.
Photoelasticity; plane photoelasticity; basic terms, basic equations, stress-optic
coefficient; isoclinic and isochromatic fringes
11.
Principal stresses separation; space photoelasticity; reflex photoelasticity
12.
Moirè method; principle, determination of stress components from moirè fringes
13.
Model similitude
Topics of seminars and laboratory work according to weeks:
1.
Safety regulations, laboratory equipment
2.
Basic relations of the theory of elasticity applied to experimental analysis
3.
Measuring of Young´s modulus using mechanical gauges
4.
Electrical resistance gauges, fixing procedure
5.
Determination of electrical resistance gauge factor
6.
Experiment preparation – plane problem
7.
Experimental stress analysis of a thin cylinder under internal pressure
8.
Experimental stress analysis of a thin cylinder under internal pressure
9.
Processing and evaluation of experimental data
10.
Photoelasticity - stress field determination for a plane model
11.
Photoelasticity - stress field determination for a plane model
12.
Strain field determination from moirè fringes
13.
Evaluation of individual assignments
List of literature:
[1]
Hearn, E. J.: Mechanics of Materials, Pergamon Press Ltd, 1985, ISBN 0-08-030529-6
[2]
Dally, J. W., Riley, W. F.: Experimental Stress Analysis, McGraw-Hill 1991,
ISBN 0-07-015218-7
[3]
Handbook on Experimental Mechanics, VCH Publishers, 1993,
ISBN 1-56081-640-6
Course name:
Course code:
Number of contact hours/week:
Mechanics 1
KME/MECH1
3 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Prof. Ing. Jiří Křen, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
written examination
Topics of lectures according to weeks:
1. Subject of mechanics, classification; kinematics of a particle, particle rectilinear motion
2. Particle curvilinear motion in a plane and in a space; kinematics of a body; translatory
motion in a plane
3. Body rotary motion, general motion in a plane, basic resolution
4. Roll centre, acceleration centre; velocity and acceleration fields; simultaneous motions of
bodies in a plane, general resolution
5. Force – determination, summation; force moment about a point and about an axis;
Varignon’s theorem; couple; fundamental theorems of statics
6. Force field, force and moment work and power; mechanical system efficiency
7. Force systems; substitution, equilibrium, equivalence; forces with a common point of
application
8. General force system, parallel forces; mass centre
9. Mounting and equilibrium of a particle in a plane and in a space including friction
10. Mounting and equilibrium of a body in a plane including friction
11. Assembling of systems; mechanisms - kinematic solution
12. Body systems - static solution; decomposition method
13. Systems with gears - static and kinematic solutions
Topics of seminars according to weeks:
1.
Particle rectilinear motion; reverse motion
2.
Particle curvilinear motion in a plane
3.
Particle curvilinear motion in a space; translatory motion of a body
4.
Rotary and general plane motion of a body; basic resolution
5.
Roll and acceleration centre determination; general resolution of body general motion
6.
Individual assignment
7.
Forces in gearing; force moment about a point
8.
Force moment about an axis; couple; work in a force field
9.
Force systems - analytical and graphical solutions
10.
Mass centre determination, force work
11.
Particle equilibrium in a plane and in a space including friction
12.
Body equilibrium in a plane - analytical and graphical solutions; friction
13.
Plane body systems - kinematic solution (analytical and graphical)
List of literature:
[1]
Meriam, J. L., Kraige, L. G.: Engineering Mechanics Statics, John Wiley & Sons, Inc.,
1998, ISBN 0-471-24164-4
[2]
Meriam, J. L., Kraige, L. G.: Engineering Mechanics Dynamics, John Wiley & Sons,
Inc., 1998, ISBN 0-471-24167-9
Course name:
Course code:
Number of contact hours/week:
Mechanics 2
KME/MECH2
2 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Prof. Ing. Vladimír Zeman, DrSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
combined examination (oral and written)
Topics of lectures according to weeks:
1. Dynamics of a mass particle; equation of motion, theorems of motion
2. Dynamics of a mass particle system; D’Alembert principle, theorems of motion
3. Dynamics of a body; mass centre, inertia matrix, momentum, moment of momentum,
kinetic energy
4. Translatory and rotary motion of a body; inertia effects on a rotor
5. Body plane motion
6. Dynamics of body systems in a plane; kinematic relations; decomposition method
7. Mass reduction method; motion theorem application
8. Methods of motion equation integration; body impact
9. Fundamentals of the theory of vibration; mathematical models of linear systems with 1
DOF; free vibration
10. Forced vibration of systems with 1 DOF; impulse, transient and amplitude characteristics
11. Vibration of systems with 2 DOF; free and harmonically excited vibrations
12. Fundamentals of analytic mechanics; virtual work principle in statics
13. Body and body system modelling by Lagrange’s equations
Topics of seminars according to weeks:
1.
Particle motion analysis by the motion equation
2.
Theorems of motion application, particle relative motion analysis
3.
D’Alembert’s principle and motion theorems for the particle system motion analysis
4.
Moments of inertia and products of inertia determination; transformation relations
5.
Body translatory motion analysis; rotor running-up and running-out
6.
Body rolling motion analysis; inertia effects on the body during plane motion
7.
Kinetic analysis of plane systems by the decomposition method
8.
Mechanism plane motion analysis by the mass reduction method; individual
assignment
9.
Computer simulation of the motion of body systems with variable ratios
10.
Eigenfrequencies and free vibrations of undamped and damped systems with 1 DOF
11.
Vibration of systems with 2 DOF; free and harmonically excited vibrations
12.
Fundamentals of analytic mechanics; virtual work principle in statics
13.
Body and body systems modelling by Lagrange’s equations
List of literature:
[1]
Hibbeler, R. C.: Engineering Mechanics Dynamics, Prentice-Hall, Inc., 1995,
ISBN 0-13-353715-3
[2]
Rao, S. S.: Mechanical Vibrations, Addison-Wesley Publishing Company, 1995,
ISBN 0-201-59289-4
[3]
Shabana, A. A.: Theory of Vibration, Springer-Verlag, 1996, ISBN 0-387-94524-5
Course name:
Course code:
Number of contact hours/week:
Mechanics of Rotary Machines
KME/MRS
2 (lecture) + 1 (seminar)
2 (self-study)
Course guarantor:
Prof. Ing. Vladimír Zeman, DrSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
oral examination
Topics of lectures according to weeks:
1. Rigid rotor dynamics; rotation about a general axis, bearing reactions, balancing
2. Rotary machine elastic seating
3. Laval’s rotor
4. Rotor with a generally mounted disc
5. Rotor with flexible bearings
6. Experimental analysis of rotor behaviour
7. Fundamentals of the linear system vibration theory; matrix form of motion equations,
eigenvalue problem for conservative systems
8. Rotor with continuously distributed mass modelling
9. Rotor modelling by FEM
10. Cambell’s diagram, critical revolutions, rotor steady vibration
11. Critical revolution computation; computer simulation of rotor behaviour
12. Balancing rotors with continuously distributed mass
13. Rotor stability
Topics of seminars according to weeks:
In the seminars students have an opportunity to apply the knowledge acquired in the lectures
to the solution of practical problems. The topics of the seminars are arranged in the same
chronological order as in the lectures.
List of literature:
[1]
Yamamoto, T., Ishida, Y.: Linear and Nonlinear Rotordynamics,
John Wiley & Sons, Inc., 2001, ISBN 0-471-18175-7
[2]
Krämer, E.: Dynamics of Rotors and Foundations, Springer-Verlag, 1993,
ISBN 3-540-55725-3
Course name:
Course code:
Number of contact hours/week:
Mechanics of Vehicles
KME/MV
2 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Doc. Ing. Jaromír Švígler, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
oral examination
.
Topics of lectures according to weeks:
1. Rolling of a vehicle wheel in a plane
2. Tyre rolling on a rigid base without and with side load
3. Static analysis of mechanisms in matrix form
4. Kinematic analysis of mechanisms in vector and matrix forms
5. Fundamentals of vehicle mechanism kinematic synthesis; kinematics of wheel suspension
and steering system
6. Synthesis of wheel suspension and steering system
7. Vibration of discrete linear systems with more DOF
8. Vibration of discrete linear systems with more DOF
9. Steady (quasi-static) motion of a vehicle on the road
10. Fundamentals of the gearing theory; wheel and rail contact; wheel and rail adhesion
11. Mounted axle; forces acting on the mounted axle; vehicle track control; free axle in
straight and curved rails
12. Rail vehicle dynamics in vertical direction; combustion engine dynamic effects
13. Vehicle stability, critical speed
Topics of seminars according to weeks:
In the seminars students have an opportunity to apply the knowledge acquired in the lectures
to the solution of practical problems. The topics of the seminars are arranged in the same
chronological order as in the lectures.
List of literature:
[1]
Ellis, J. R.: Vehicle Dynamics, Business Books Ltd., London, 1969
[2]
Schiehlen W.(Ed.) : Multibody Systems Handbook, Berlin u.a., Springer-Verlag
Course name:
Course code:
Number of contact hours/week:
Mechanics of Materials 1
KME/PP1
3 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Prof. Ing. František Plánička, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
written examination
Topics of lectures according to weeks:
1.
Introduction; basic terms and assumptions; stress, strain
2.
Tensile test; Hooke’s law; allowable working stress
3.
Second moments of area, parallel axis theorem, Mohr’s circle
4.
Bending; shearing force and bending moment diagrams; simple bending theory
5.
Slope and deflection of beams; direct integration method, Mohr’s method
6.
Deflection of beams with variable cross-sections; statically undetermined beams
7.
Torsion; simple torsion theory
8.
Complex stresses; two-dimensional stress systems; Mohr’s circle, principal stresses
9.
Complex stresses, three-dimensional stress systems, principal stresses, Hooke’s law,
strain energy
10.
Theories of elastic failure; maximum shear stress theory, maximum shear strain energy
per unit volume (distortion energy) theory, Mohr’s modified shear stress theory for
brittle materials
11.
Combined loading; eccentric tension, skew bending, bending-torsion, tension-torsion
12.
Strains beyond the elastic limit - introduction to plasticity
13.
Fundamentals of experimental stress analysis
Topics of seminars according to weeks:
1.
Tension, compression, allowable working stress, elongation; rope loading
2.
Thin rotating rings, rotating rods; conical rods
3.
Simple statically undetermined problems; prestressed screws
4.
Second moments of area
5.
Shear force and bending moment diagrams; allowable stress
6.
Shear stress in bending; deflection - direct integration method; individual assignment
7.
Deflection - Mohr’s method
8.
Statically undetermined beams
9.
Torsion - circular and rectangular cross-sections
10.
Complex stresses; 2D and 3D stress systems
11.
Theories of elastic failure
12.
Combined loading
13.
Plastic bending, plastic torsion
List of literature:
[1]
Spiegel, L., Limbrunner,G. F.: Applied Statics and Strength of Materials, Macmillan
Publishing Company, 1991, ISBN 0-675-21123-9
[2]
Hearn, E. J.: Mechanics of Materials, Pergamon Press Ltd, 1985, ISBN 0-08-030529-6
[3]
Singer, F. L., Pytel, A.: Strength of Materials, HARPER&ROW, New York, 1980,
ISBN 0-06-046229-9
[4]
Sochor, M.: Strength of Materials I, CVUT Prague, 1998, ISBN 80-01-01859-8
Course name:
Course code:
Number of contact hours/week:
Mechanics of Materials 2
KME/PP2
3 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Doc. Ing. Vladislav Laš, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
combined examination (oral and written)
Topics of lectures according to weeks:
1. Introduction to the advanced theory of elasticity
2. Potential energy, energy of external and internal forces, system potential energy;
variation principles
3. Finite element method - introduction, general approach; 2D element
4. Structure analysis; body stiffness matrix; elements
5. Rotating discs, stress and strain
6. Thick-walled cylinders under internal pressure
7. Thin curved beams
8. Frames; struts
9. Introduction to fracture mechanics; LEFM, stress intensity factor, fracture toughness
10. Mechanics of composites; classification, constitutive relations, transformation of stresses
and strains
11. Off-axis stiffness of unidirectional composites; laminates, plane stiffness of symmetrical
laminates; stress-strain relation
12. Failure criteria for orthotropic materials; maximum stress theory, maximum strain theory
13. Introduction to fatigue; fatigue limits for materials and real components
Topics of seminars according to weeks:
1.
Mechanics of materials I revision
2.
Laboratory measurement #1
3.
Laboratory measurement #2
4.
Computational system RELAX; assignment of individual tasks
5.
Work on individual assignments
6.
Rotating discs
7.
Thick-walled cylinders
8.
Discs on shafts, critical revolutions
9.
Curved beams
10.
Frames
11.
Struts
12.
Composites
13.
Fatigue; evaluation of individual assignments
List of literature:
[1]
Hearn, E. J.: Mechanics of Materials, Pergamon Press Ltd, 1985, ISBN 0-08-030529-6
[2]
Kanninen, M. F., Popelar, C. H.: Advanced Fracture Mechanics, Oxford University
Press, New York, 1985, ISBN 0-19-503532-1
[3]
Berthelot, J-M.: Composite Materials, Springer-Verlag, 1999, ISBN 0-387-98426-7
[4]
Sochor, M.: Strength of Materials II, CVUT Prague, 2001, ISBN 80-01-02299-4
Course name:
Course code:
Number of contact hours/week:
Theory of Plasticity
KME/TP
2 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Prof. Ing. František Plánička, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
oral examination
Topics of lectures according to weeks:
1. Stress analysis, stress tensor, mean stress tensor, deviator stress tensor, invariants of stress
tensor
2. Invariants of deviator stress tensor, effective stress, volumetric and distortion energies;
strain analysis, effective strain
3. Engineering and true stress, true stress – strain diagrams; substitutions of stress-strain
curves (elastic-ideally plastic, rigid-ideally plastic, elastic-plastic with linear hardening
materials)
4. Tension and compression of rods beyond the yield point
5. Plastic bending, residual stresses
6. Plastic bending, residual stresses
7. Tresca yield criterion
8. Von Mises yield criterion
9. Axisymmetric solids; plastic behaviour of rotating discs and thick cylinders; residual
stresses
10. Axisymmetric solids; plastic behaviour of rotating discs and thick cylinders; residual
stresses
11. Yield surface, loading path in stress space, simple and combined loading
12. Theories of plasticity; deformation theory, incremental or flow theory
13. Plastic torsion; circular and non-circular profiles
Topics of seminars according to weeks:
In the seminars students have an opportunity to apply the knowledge acquired in the lectures
to the solution of practical problems. The topics of the seminars are arranged in the same
chronological order as in the lectures.
List of literature:
[1]
Hearn, E. J.: Mechanics of Materials, Pergamon Press Ltd, 1985, ISBN 0-08-030529-6
[2]
Chen, W. F., Zhang, H.: Structure Plasticity Theory, Problems and CAE Software,
Springer-Verlag, ISBN 0-387-96789-3
[3]
Chen, W. F., Han, D. J.: Plasticity for Structural Engineers, Springer-Verlag,
ISBN 0-387-96711-7
Course name:
Course code:
Number of contact hours/week:
Selected Parts of Mechanics and Elasticity
KME/VSMP
3 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Prof. Ing. Vladimír Zeman, DrSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
oral examination
Topics of lectures according to weeks:
1. Theory of flat rectangular plates; internal moments; basic differential equation; boundary
conditions
2. Analytical solution of the differential equation of plate displacement by indefinite series
3. Ritz’s variation method; plate displacement determination
4. Beams on elastic foundations; indefinite and semi-definite beams; finite length beams
5. Contact problems; line contact; force acting on a semi-indefinite space
6. Contact problems; uniform and non-uniform loading on a circular area
7. Methods for assembling motion equations in machine dynamics
8. Discrete models of vibrating mechanical systems
9. Discretization of one-dimensional continuum by FEM (rod, shaft, beam)
10. Discretization of structures by FEM
11. Modal analysis of vibrating mechanical systems
12. Modal method for forced vibration analysis
13. Steady harmonically excited vibrations
Topics of seminars according to weeks:
1.
Theory of flat circular plates
2.
Basic symmetrical loads of circular plates
3.
Combined loading of circular plates
4.
Flat rectangular plates – Ritz’s method
5.
Solution of the problem of definite length beams by Krylov’s functions
6.
FEM for flat plate simple problem modelling
7.
Decomposition method in the dynamics of machines
8.
Principle of virtual work and Lagrange’s equations for the motion analysis of
mechanisms
9.
Modelling of drive system torsion vibration
10.
Beam discretization
11.
Plane frame discretization
12.
Modal analysis of selected mechanical systems with 2 DOF
13.
Drive system enforced vibration
List of literature:
[1]
Hearn, E. J.: Mechanics of Materials, Pergamon Press Ltd, 1985, ISBN 0-08-030529-6
[2]
Boresi, A. P., Sidebottom, O. M., Seely, F. B., Smith, J. O.: Advanced Mechanics of
Materials, JOHN WILEY AND SONS,1978, ISBN 0-471-08892-7
[3]
Cook, R. D.: Finite Element Modeling for Stress Analysis, JOHN WILEY AND
SONS, 1994, ISBN 0-471-10774-3
[4]
Rivin, E. I.: Stiffness and Damping in Mechanical Design, Marcel Dekker, Inc.,
New York, Basel, 1999, ISBN 0-8247-1722-8
[5]
Shabana, A. A.: Theory of Vibration, Springer-Verlag, 1996, ISBN 0-387-94524-5
Course name:
Course code:
Number of contact hours/week:
Service Life and Reliability of Structures
KME/ZS
2 (lecture) + 2 (seminar)
2 (self-study)
Course guarantor:
Prof. Ing. František Plánička, CSc.
Requirements for the successful completion of the course:
Continuous assessment:
individual assignments
Final assessment:
oral examination
Topics of lectures according to weeks:
1. Limited states of structures; classification; fatigue; basic terms, fatigue influenced factors
2. Fluctuating loading; classification; harmonic loading
3. Statistical methods in fatigue; S-N curve; Smith’s and Haigh’s diagrams
4. Structure loading, recording and processing; correlation analysis processing
5. Processing using characteristic parameters; peaks and ranges methods, rain-flow method
two-parameters processing
6. Unlimited fatigue life
7. Limited fatigue life; high-cycle fatigue; fatigue damage cumulation hypotheses
8. Shortened fatigue tests
9. Low-cycle fatigue; soft and hard loading, life curves; notched bodies in the elastic-plastic
state
10. Stress and strain concentration in notched bodies; durability of notched bodies
11. Fatigue crack propagation; Paris-Erdogan equation
12. Experimental verification of structure fatigue life
13. Fundamentals of mechanical systems reliability
Topics of seminars according to weeks:
In the seminars students have an opportunity to apply the knowledge acquired in the lectures
to the solution of practical problems. The topics of the seminars are arranged in the same
chronological order as in the lectures.
List of literature:
[1]
Hearn, E. J.: Mechanics of Materials, Pergamon Press Ltd, 1985, ISBN 0-08-030529-6
[2]
Osgood, C. C.: Fatigue Design, John Wiley & Sons, Inc.,1970, ISBN 0-471-65711-5
[3]
Manson, S. S.: Thermal Stress and Low-cycle Fatigue, McGraw-Hill, Inc., 1966
[4]
O’Connor, P. D. T.: Practical Reliability Engineering, John Wiley & Sons, 1991,
ISBN 0-471-92696-5