Linear Vibrations

Teaching staff

Additional information

De­scrip­ti­on

Many vibration problems in engineering can be described in a very good approximation by linear differential equations, so that the theory of linear differential equations, which is very well developed in terms of mathematics, can be applied.

The lecture shall give an introduction to common methods for the treatment of linear dynamical systems. First, general vibration systems with N degrees of freedom are treated. Then the dynamics of systems in state space will be discussed.

The lecture continues the En­gi­nee­ring Vi­bra­ti­ons and serves as preparation and basis for further courses, especially Nonlinear Vibrations.

To­pics

  • Introduction
  • Time-invariant dynamical systems with N degrees of freedom (MDGKN systems): eigenvalue theory, Rayleigh quotient, specific behavior of MK, MDK, MDGK, MKN systems, methods for determination of particulate solutions
  • Representation in the state space: general properties, geometry of the state space near rest positions, solution by means of fundamental matrix, eigenvalue theory, Jordan transformation, methods for the determination of particulate solutions

Li­te­ra­tu­re

  • P. Hagedorn: Technische Schwingungslehre, Springer-Verlag, (1. Auflage 1987)
  • P. Hagedorn, D. Hochlenert: Technische Schwingungslehre, Europa-Lehrmittel (2. Auflage 2014)
  • J. Wittenburg: Schwingungslehre, Springer-Verlag (1. Auflage 1996)
  • W. Walter: Gewöhnliche Differentialgleichungen, Springer-Verlag (7. Auflage 2000)
  • P. Hagedorn: Technische Schwingungslehre Band 2, Springer-Verlag (1. Auflage 1989)
  • P. Hagedorn, A. DasGupta: Vibrations and Waves in Continuous Mechanical Systems, Wiley (1. Auflage 2007)
  • J. Wauer: Kontinuumsschwingungen, Springer-Verlag (2. Auflage 2014)
  • D. Gross, W. Hauger, P. Wriggers: Technische Mechanik – Band 4, Springer-Verlag (9. Auflage 2014)