Lecturer(s)


Zeman Vladimír, Prof. Ing. DrSc.

Vimmr Jan, Doc. Ing. Ph.D.

Course content

1. Dynamics of a rigid body. Equations of motion and inertia forces. Rotor dynamic balancing. Reactions at the rotor support. 2. Spherical motion of a rigid body. Kinetic energy, inertia forces, reactions at the gyroscope support. 3. Plane, spatial and screw motion of a rigid body. Kinetic energy, inertia forces and reactions at the support. 4. Dynamics of multibody systems. Number degrees of freedom. Kinetic solving. 5. Balancing of mechanisms. Centric and excentric body impact, submission of the credit problem. 6. Mathematical modelling of multibody, system motion using Lagrange´s equations. Irregularity of machine running. 7. Mathematical modelling of multibody system motion using Lagrange´s equations of mixed type. Computer simulation of motion. 8. Principles of vibration theory. Mathematical models of linear systems with one degree of freedom. Longitudinal, torsional and bending free vibration. 9. Forces vibration of linear systems with one degree of freedom. Transient vibration and steady vibration under harmonic and periodic excitation. Method of Laplace transformation. Forced vibration excited by rotating imbalance and kinematicaly. 10. Mathematical modelling of linear systems whit two and more degrees of freedom in the matrix form. Natural frequencies and modes. Spectral and modal matrices. 11. Modal method for investigation of free and forced vibration of undamped linear systems with more degrees of freedom. Calculation of dynamic response of undamped system with two degrees of freedom. 12. Modelling of onedimensional continuum vibration using finite element method. Transverse vibrations of the beams. 13. Steady vibration caused harmonic and periodic excitation. Frequency characteristics. Steady harmonic vibration of frame.

Learning activities and teaching methods

Lecture, Practicum
 Preparation for an examination (3060)
 60 hours per semester
 Undergraduate study programme term essay (2040)
 40 hours per semester
 Contact hours
 65 hours per semester

prerequisite 

professional knowledge 

Student knows  statics and kinematics of mass points and rigid bodies,  dynamics of mass points,  vector and matrix calculus  principles of linear algebra,  principles of differential and integral calculus. 
learning outcomes 

Student  classifies a rigid body motion in term of kinematics for investigation of its dynamic properties,  applies the method of dynamic equilibrium and Lagrange´s equations for investigation of mechanical system motion,  analyses dynamic properties of mechanisms,  investigates the vibrations of mechanical systems with one or more degrees of freedom. 
teaching methods 

Lecture 
Practicum 
assessment methods 

Oral exam 
Seminar work 
Recommended literature


BROUSIL, J.  SLAVÍK, J.  ZEMAN, V. Dynamika. 1. vyd. Praha : SNTL, 1989. ISBN 8003001641.

Hibbeler, R. C. Engineering mechanics : dynamics. 11th ed. Singapore : Prentice Hall, 2007. ISBN 9780132038096.

Janeček, Otakar; Zeman, Vladimír. Technická dynamika. 2. přeprac. vyd. Plzeň : VŠSE, 1973.

Zeman, Vladimír. Dynamika v příkladech. reedice. Plzeň : ZČU, 1997. ISBN 8070822929.
