Natural frequency of large degree of freedom system

AI Thread Summary
The discussion centers on a spring-mass system comprising 200 masses and 199 springs, each mass weighing 100 tonnes with a stiffness of 20 MN/m. The calculated lowest natural frequency is 0.0124 Hz, but the wave speed calculated at 141.4 m/s suggests a wave frequency that is more than double the natural frequency. Participants clarify the stiffness unit as 20 MN/m and inquire about the connection configuration of the masses and springs. The conversation concludes with the original poster confirming the stiffness unit and indicating that the issue has been resolved.
dxdy
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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?
 
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How did you calculate the speed of the wave in this system? And what kind of wave?
 
dxdy said:
masses are 100 tonnes and stiffness 20 MN.
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?
 
Yes I did mean 20 MN/m.
Solved.
 
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