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Vibration Theory I: Receptance

  • John D. Robson
  • Colin J. Dodds
  • Donald B. Macvean
  • Vincent R. Paling
Part of the International Centre for Mechanical Sciences book series (CISM, volume 115)

Abstract

When the configuration of a mechanical system is completley described by one independent variable x, it is said to have one degree of freedom. This quantity usually has the dimension of length or angle. In a real system there will be inertia forces depending on the second time derivative ẍ, viscous damping forces depending on the velocity ẋ, and restoring forces depending on x. The equation governing the vibration can usually be brought into the form
(1)
, where the periodic excitation P(t) is regarded as the input to the system and the resulting motion x(t) the response. It should be noted in passing that in requiring the forcing term P(t) to appear alone in (1) we have ruled out the case of parametric excitation. The system is said to be linear when equation (1) can be written in the standard form
(2)
, i.e. when no higher power of x, ẋ, ẍ occurs. (The system is still linear when either of the two parameters in (2) varies with time. However, we will exclude such cases here).

Keywords

Elastic Foun Dation Parametric Excitation Complex Response Displacement Output Periodic Excitation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • John D. Robson
    • 1
    • 2
  • Colin J. Dodds
    • 1
  • Donald B. Macvean
    • 1
  • Vincent R. Paling
    • 1
  1. 1.University of GlasgowUK
  2. 2.UdineItaly

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