Dynamics V - Selected Chapters (FSI-R5D)

The aim of the course is to introduce students to selected parts of dynamics, specifically rotor system dynamics and reduction methods. The course also aims at a practical and theoretical analysis of machine noise, and computational modeling of their components in order to reduce their vibration and radiated acoustic energy.

Students will acquire basic theoretical knowledge in the field of rotor systems, degrees of freedom reduction, and acoustics. They will learn about the computational modeling of the rotors. They will learn to predict the resonant states and critical speeds of rotating machines and learn how to suppress them. Students will be able to reduce systems with many degrees of freedom, thus reducing computational time. Graduates will be able to analyze machine noise, identify sources of vibration and noise, and implement active and passive methods of vibration and noise reduction. Students will acquire basic knowledge of optimization.

In the course, students will be acquainted with the basic dynamic properties and dynamic behavior of the components and parts of rotor systems. Specifically, with the shaft, non-linear constraints between the rotating and non-rotating parts, turbine and compressor blades, and disks. Special attention is paid to the rotor eigen frequencies, mode shapes, and critical speed prediction. Some tasks can be computationally demanding, especially in time-domain solutions. Therefore, students will be introduced to methods of reducing degrees of freedom. The course will also pay attention to vibrations and noise, which are accompanying phenomena of the working processes of all machinery. The course is focused on the basics of acoustics, measurement of acoustic quantities, and computational modeling of vibroacoustic systems. In the exercises, students will be introduced to the solution of vibroacoustic problems using numerical methods.

Active participation in seminars, obtaining a minimum of 50 points (out of 100 possible) in the final test of the basic knowledge and solution of typical tasks from profiling areas of the subject. The specific form of the tests, types and number of exercises or questions, and details of assessment will be given by the lecturer during the semester. The final assessment is based on the ECTS scale.

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.

• Introduction to rotordynamics, basic models of rotors


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


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


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


• Vibration of bladed disks, Campbell diagram


• Vibration of the undamped rotor with gyroscopic effects


• Rotor balancing


• Acoustic quantities, wave equation and its solution, mechanical and aerodynamic noise sources


• Measurement of acoustic quantities


• Deterministic models of vibroacoustic systems: finite element method (FEM), boundary element method (BEM)


• Statistical models of vibroacoustic systems (statistical energy analysis SEA), hybrid models (FEM + SEA)

• Calculation of critical speed using simple rotor models


• Simulation of starting of electric motors in time domain


• Simulation of electric motor start in frequency domain


• Simulation of rotor bearing behavior


• Vibration of disks and bladed disks


• Modeling of bladed disks using cyclic symmetry


• Effect of nonlinearities in bladed discs dynamic behavior


• Propagation of acoustic waves in free and enclosed space


• Radiation of acoustic waves from vibrating body to free space, radiated acoustic power


• Propagation of acoustic waves from a vibrating body into a acoustic cavity


• Transmission of acoustic waves across different types of walls

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

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