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Natural frequency of large degree of freedom system

  1. Oct 21, 2011 #1
    I have a spring-mass system with 200 masses and 199 springs. All masses are 100 tonnes and stiffness 20 MN. The boundary conditions are fixed-free.

    I have constructed a lumped mass matrix and stiffness matrix and calculated the lowest natural frequency. Including the boundary conditions I calculated this to be 0.0124 Hz.

    However, when I calculate the wave speed, I can calculate the period of the wave starting at one end, reflecting at the free end and returning. This frequency (1/T) is more than double the natural frequency I calculated. The wave speed I calculated was 141.4 m/s assuming the distance between masses is 10 metres.

    Am I using the wrong approach here for calculating the natural frequency both ways?
  2. jcsd
  3. Oct 21, 2011 #2
    How did you calculate the speed of the wave in this system? And what kind of wave?
  4. Oct 21, 2011 #3


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    What does it mean stiffness 20MN? You, maybe, meant 20 MN/m?
    And how are they connected? In a simple chain mass-spring-mass-sping-mass....mass-spring-mass, or rather in some mesh?
  5. Oct 21, 2011 #4
    Yes I did mean 20 MN/m.
    Last edited: Oct 21, 2011
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