Dynamics V - Selected Chapters (FSI-R5D)

The course aims to introduce students to selected issues of dynamics of rotor systems, and the ways of obtaining information about the dynamic behavior of rotating machines from vibration measurements of rotating machines.

Studenti získají teoretické znalosti z oblasti rotorových soustav, seznámí se s možnostmi výpočtového modelování, naučí se predikovat rezonanční stavy a kritické otáčky rotačních strojů a seznámí se s možnostmi zmírnění jejich projevů. Studenti se naučí zpracovat data získané měřením vibrací rotačních strojů.

Students must be able to solve the eigen value problem, solve the response in forced, steady and transient oscillations of systems with n degrees of freedom. Furthermore, the students must to have knowledge of the basics of nonlinear vibrations, and knowledge of the basics of experimental modal analysis. The student must know, matrix calculus, linear algebra, differential equations, fundamentals of the finite element method.

In the course, students will be introduced to selected problems in the field of dynamics of rotating systems. In addition to the dynamic behavior of individual parts of rotor systems, students will be introduced to the computational modelling of nonlinear couplings between rotating and non-rotating parts as well as between blades and disks. The basic dynamic properties that will be discussed in the course will include the determination of natural frequencies and modes of vibration of rotors and disks and the determination of critical machine speeds. The course will also introduce students to the processing of vibration measurement data from rotating machines.

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

Active participation in the course, obtaining at least 20 points (out of 40 possible), which can be received by completing tasks and achieving at least 30 points (out of 60 possible) in the test. The specific form of the tests, types, number of tasks or questions and details of the assessment will be given by the lecturer during the semester. The final evaluation is given by the sum of the points according ECTS. For successful completion of the course it is necessary to obtain at least 50 points.

Attendance at practical training is obligatory. Longer absence is compensated for by special tasks according to instructions of the tutor. Seminar credits are awarded on the condition of: active presence in the seminars, good results of seminar tests on basic knowledge, solution of additional tasks in case of longer excusable absence. Seminar tutor will specify the concrete form of these conditions in the first week of semester.

• Undamped Laval (Jeffcott) rotor in rigid and flexible bearing supports


• Laval (Jeffcott) rotor with external and internal damping. Rotor stability


• Rotor oscillation with consideration of gyroscopic effects


• Joints between rotating and non-rotating parts (bearings, shock absorbers, sealing joints).


• Vibration of bladed disks, Campbell diagram


• Effect of non-linearities on the dynamic properties of rotors and bladed disks


• Processing of vibration measurement data of rotating machines.

• Simulation of rotor start up in time domain


• Simulation of rotor behaviour in bearings


• Vibrations of disks and bladed disks


• Effect of nonlinearities on the dynamic behaviour of bladed discs


• Processing of vibration measurement data of rotating machines.

Erwin Kramer: Dynamics of Rotors and Foundations , Springer Verlag, 1993

Gasch, Pfutzner: Dynamika rotorů, SNTL Praha, 1980.