# Natural frequency of large degree of freedom system

1. Oct 21, 2011

### dxdy

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. Oct 21, 2011

### nasu

How did you calculate the speed of the wave in this system? And what kind of wave?

3. Oct 21, 2011

### xts

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?

4. Oct 21, 2011

### dxdy

Yes I did mean 20 MN/m.
Solved.

Last edited: Oct 21, 2011