Can dynamic equivalent stiffness matrix sigularity??

Dear all, I have two questions boring me.

  1. In finite element dynamic analysis. The structrural equivalent stiffness matrix, Ke=K+2/h*C+4/h^2*M, can become sigularity?? I kown that in static analysis the structrural stiffness matrix can be sigularity with Det(K) = 0.

2.In finite element dynamic analysis (note: not in static). If a beam is no any restraints, I can directly analyse it under a force using the Newmark method?? I try this, I think it can be work, am I wrong??

Many thanks.

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For an unrestrained structure, K is singular, but Ke will not be singular, in general, if you have a physically reasonable distribution of mass. Thus, there is no problem, in principle, with doing dynamic analysis of unrestrained structures.

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Good! I want to get a more definied answer.

This means that the Ke is always positive-definite matrix, and never become a negative definite matrix??

And so the so-called Arc-Lengh method which to overcame load limit point to negative stiffness region can be only useful in static analysis (because K can become singular)??

I think it right??

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