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portal frame approximation to pendulum

portal frame approximation to pendulum

portal frame approximation to pendulum

(OP)
How do I approximate a portal frame to a pendulum?

   EI    Lumped mass
!--------!( o -> )      !
!        !              !
!EI      !EI            !2EI
!        !              !
-        -              -
Specific beam, column sections with mass and weight.

So, here are my concerns for some portal frames:
1)P.F.(portal frame) with 1 DOF;
2)P.F. with 1 DOF plus 1 lumped mass;
3)P.F. with 2 DOF
4)P.F. with 2 DOF plus 1 lumped mass acting on the top level;
5)P.F. with 2 DOF plus 2 lumped masses acting on every level;

The correspondance between the P.F. and the pendulum regarding the mom. of inertia (I) and modulus of elasticity (E)is given below:

    P.F.          Pendulum
1gld           - 2I;        
1gld+1lumped mass  - 2I+2E;
2gld           - 2I+2E;     
2gld+1lumped mass  - 2I+4E;
2gld+2lumped masses- 2I+4E;

In order to obtain similar fundamental periods (in the 1st mode of vibration) I had to do the up approximations.
I thought only a EI <=> 2EI approximation would be necessary, but as you can see sometimes I made EI <=> 4EI approx. Does this approx. depends on the number of DOFs?
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RE: portal frame approximation to pendulum

(OP)
I mean, is this correct??

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