Time History Analysis Of 2D Frame Using MATLAB (El Centro)

[JonathanDavis]

Hi,
Consider a 2D frame like below which excited by el Centro earthquake:

I'm Using Direct Time Integration To obtain response of structure. I verified my program with SAP200 when a Harmonic load applied in node2 and results are the same. but in this case, i.e. base excitation, i have a problem. Consistent Mass Matrix used here and following relation used in order to obtain nodal forces due to base excitation:
{fg}=-[M]*{Ag}*Ug
and We know that:
[M]{A}+[C]{V}+[K]{D}={fg}
in which [M]=Consistent Matrix (6x6 in this case), {Ag} = Influence Vector (6x1) which is zero except for horizontal degrees of freedom, i.e 4 & 7 that equals to 1. in other words {Ag}=[1,0,0,1,0,0].also Ug is a scalar number that equals to earthquake record data at time t. I wonder if this is Right or Wrong? i know somethings wrong with this because i can't get correct results. I really appreciate if you help me.
thanx...

 

[GregLocock]

what units is Ug in?

Cheers

Greg Locock


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[JonathanDavis]

Ug in m/sec2 (earthquake acceleration)

 

[GregLocock]

OK. and if you apply the resulting fg time histories to your model, do you get the correct acceleration time histories {A}

Cheers

Greg Locock


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[JonathanDavis]

No...The Result differs from SAP.I know something's wrong with {fg}. I didn't find anything in Structural Dynamics books. most of them use modal analysis to this kind of analysis.

 

[GregLocock]

In that case your maths is wrong. in a linear system if you apply the accelerations to get the forces, then if you apply the forces you should get the accelerations.

Cheers

Greg Locock


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[JonathanDavis]

thanx. Do you know a book,source or a computer program to find the right mathematical formulation?

 

[GregLocock]

Sorry, not really. I'd derive it from first principles.

Cheers

Greg Locock


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[bkal]

It is not clear what is your mass matrix [M]; i.e. is it a global mass matrix, elemental mass matrix or just part attributed to the driven node?

One quick way to solve this (very crude) is to attach a large mass to your nodes 1 and 2, and then drive that mass with a force equal to "Large mass" * "ground acceleration".

 

[aouiche]

I have the same probleme and i think that the problem is to use technique such static condensation méthod to resolve system

 

[IDS]

Do you know a book, source or a computer program to find the right mathematical formulation?

It might take some finding, but it must be in Opensees somewhere.

http://opensees.berkeley.edu/

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/