Course detail

Computer Methods in Dynamics

FSI-RPMAcad. year: 2015/2016

The course is intended for the students of the 4th year of study at the Faculty of Mechanical Engineering. It focuses on vibration of mechanical systems. Numerical methods are applied to solve the tasks with the help of PC. The lectures deal with analytical dynamics of discrete systems, forced oscillations of mechanical systems with one degree of freedom, vibration of discrete mechanical systems with n-degrees of freedom, reduction of degrees of freedom, vibration of continuous systems, approximate methods of solution of continuous systems (Raleigh’s method, Ritz method), direct integration methods (method of central differences, Runge-Kutta method, Houbolt method, Wilson theta method, Newmark method), tuning of mechanical systems, using of topology by modelling of mechanical systems The aim of the course is to provide students with good knowledge of oscillation of mechanical systems and the possibility to solve them by using numerical methods.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Eduard Malenovský, DrSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Learning outcomes of the course unit

Students are expected to have the following knowledge when they begin the course “Computer methods in mechanics I”: linear algebra, differentiation, integration, solution of differential equations, matrix arithmetic, basic programming, particular mathematical software (MAPLE or MATLAB), basic statistics, elasticity of continuous systems, fundamental principles of dynamics, formation of kinetic equations of translational torsional and general plane motion and solution of free oscillating systems with one degree of freedom.

Prerequisites

Students are expected to have the following knowledge when they begin the course “Computer methods in mechanics I”: linear algebra, differentiation, integration, solution of differential equations, matrix arithmetic, basic programming, particular mathematical software (MAPLE or MATLAB), basic statistics, elasticity of continuous systems, fundamental principles of dynamics, formation of kinetic equations of translational torsional and general plane motion and solution of free oscillating systems with one degree of freedom.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Participation in the lessons is required and systematically controlled by the teacher. One absence can be compensated by attending a seminar with another group in the same week, or by elaboration of compensatory tasks. Longer absence can be compensated by special tasks assigned by the tutor. Credit requirements: active participation in the seminars; good results in seminar tests testing basic knowledge; solution of additional tasks in case of longer excusable absence. Seminar tutor will specify the form of such conditions in the first seminar.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The course familiarises students with methods of determination of the natural frequencies and modal vectors of discrete and continuous systems. The methods can be applied to diminish the vibration and noise of machines.

Specification of controlled education, way of implementation and compensation for absences

The examination requires knowledge of substance of the lectured matters. Examination has two parts - oral and written. The students can use the notes from lectures and seminars. The examination is classified according the Rules for Study and Examination valid at the Brno University of Technology.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Slavík,J.,Stejskal,V.,Zeman,V.: Základy dynamiky strojů, ČVUT Praha, 2000.
Harris,C., Piersol, A., G.: Shock and Vibration Handbook, McGRAW-HILL New York, 2002.

Recommended reading

Meirovitch,L.: Elements of Vibration Analysis, 2002

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-IMB , 1. year of study, winter semester, compulsory
    branch M-MET , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

prof. Ing. Eduard Malenovský, DrSc.

Syllabus

1. Modelling of mechanical systems. Introduction to analytical mechanics.
2. Vibration of n-degree of freedom systems.
3. Frequency determinant, Jacobi’s eigenproblem. Choleski and Householder meth.
4. Raleigh’s quotient, physical and Lanczos reduction of mech. systems.
5. Free and forced vibration of damped mechanical systems. Proportional damping.
6. Longitudinal and torsional vibrations of bars.
7. Bending vibration of beams. Lagrange function, method of transfer matrices.
8. Vibration of rectangular and circular membranes, nodal lines.
9. Vibration of rectangular and circular plates.
10.Approximation solution of continuous systems. Rayleig and Ritz method. FEM.
11.Direct integration methods of dif. equations.
12.Nonlinear vibrations, equivalent and direct methods of linearization.
13.Tuning of mechanical systems. Using of topology to construct equation of motion.
seminars in computer labs

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

Ing. Lubomír Houfek, Ph.D.

Syllabus

1. Computational analysis of eigen frequency of torsion systems
2. Computational analysis of eigen shapes of vibration of torsion systems
3. Computational analysis of impulse function of vibration of torsion systems
4. Computational analysis of steady state response of vibration of torsion systems
5. Computational analysis of transient response of vibration of torsion systems
6. Sensitivity analysis and spectral tuning of vibration of torsion systems
7. Computational analysis of eigen frequency of lateral vibration of beams
8. Computational analysis of eigen shape of lateral beam vibrations
9. Computational analysis of steady state response of lateral beam vibrations
10. Computational analysis of unsteady response of lateral beam vibrations
11. Experimental analysis of lateral beam vibrations - shaker - I. part
12. Experimental analysis of lateral beam vibrations - shaker - II. part
13. Experimental analysis of lateral beam vibrations - exp. modal analysis