Natural frequency of large degree of freedom system

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Discussion Overview

The discussion revolves around the calculation of the natural frequency of a large spring-mass system with multiple degrees of freedom, specifically a system comprising 200 masses and 199 springs. Participants explore the relationship between the calculated natural frequency and wave speed, considering boundary conditions and system configuration.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant calculated the lowest natural frequency of their system to be 0.0124 Hz, based on a lumped mass matrix and stiffness matrix.
  • The same participant noted a discrepancy between the natural frequency and the frequency derived from wave speed calculations, which resulted in a frequency more than double the natural frequency.
  • Another participant inquired about the method used to calculate the wave speed and the type of wave being considered.
  • A third participant questioned the meaning of the stiffness value provided, suggesting it might be intended as 20 MN/m and asked for clarification on the connection configuration of the masses and springs.
  • The original poster confirmed the stiffness value as 20 MN/m and indicated that the issue was resolved.

Areas of Agreement / Disagreement

There is no consensus on the approach to calculating the natural frequency and wave speed, as participants have raised questions and clarifications without reaching a definitive resolution.

Contextual Notes

The discussion does not clarify the assumptions made in the calculations or the specific configuration of the mass-spring system, which may affect the results.

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.
 
Last edited:

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