Dynamics of Machines and Structures

In order to meet the demand for increased performance and efficiency, modern designs focus mainly on achieving higher rates of revolution and lighter structures, leading in many cases to contra-productive vibrations in the main structure or components.

This module deals with techniques for generating mathematical models describing the vibration parameters of an elastic structure. The results are useful in enhancing the dynamic behaviour of a structure, and combining them with measured normal modes parameters provides strategies for further optimisation.

  1. Representation of Signals, Excitation Functions and System Response

    • Fourier Series
    • Fourier Transform

  2. Analysis of Single Degree of Freedom Systems (1DOF)

    • equation of motion / linearisation / variational equation
    • free vibrations / eigenvalues
    • excited vibration / resonance
    • harmonically excited systems (1DOF)
    • periodically excited systems (1DOF)
    • arbitrary transient excited systems (1DOF)

  3. Analysis of Multi-Degree-of-Freedom Systems (nDOF)

    • equation of motion / Lagrange's Equation
    • discretisation of continua
    • structural matrices (M, G, D, K)

  4. Modal analysis

    • eigenvalue and eigenvector calculation
    • orthogonality and normalisation of eigenvectors
    • modal mass, stiffness and damping matrices
    • generalised co-ordinates
    • modal parameter in the frequency domain
    • frequency response analysis

  5. Torsional Vibration Analysis/ Rotordynamics

    • mathematical modelling
    • torsional vibration of continuous systems
    • free vibration of discrete systems
    • forced response of discrete systems
    • simulation of torsional vibration at drive trains

  6. Lateral Vibration of Rotating Shafts / Rotor Dynamics

    • mathematical modelling
    • lateral vibration of continuous systems
    • free vibration of discrete systems
    • forced response of discrete systems
    • balancing of rotors
    • influence of bearings and seals
    • gyroscopic effect on rotating shafts

  7. Some Aspects of Non-linear Vibration

    • stability of motion
    • phase plane portrait / singular points / limit cycle
    • self-excited oscillations
    • non-linear characteristics / response curves
    • parameter - excited vibration
    • some remarks on chaotic vibration

  8. Practical exercises with the following software:

    • Mathcad; Matlab/Simulink: eigenvalues / eigenvectors calculation, simulation of dynamic systems
    • ITI-Sim3.1: simulation of dynamic systems
    • Nastran: FE - analysis
 
    Home  | CAME  | Structure and Curriculum  | Admission Requirements  | Course Guide  | Application  | About Bielefeld / Flensburg  | Contact