In several articles that use scaled models, they always talk about this: "Because the system under consideration is a scaled model, the earthquake must be reproduced at five times the recorded rate." What did they mean ?
- See the attached article page 11.
It is because when scaled models are used, the relation between parameters such as inertial forces and frequency change. These are known as similitude laws (Cauchy and Froude similitudes)
You can find information about this relations in:
Lourenço, P.B.; Avila, L.; Vasconcelos, G.; Alves, J.P.; Mendes, N.; Costa, A.C. (2013): Experimental investigation on the seismic performance of masonry buildings using shaking table testing. Bulletin of Earthquake Engineering, 11,1157-1190.
The results obtained from the scaled structure or the prototype will be equivalent to those obtained by the dynamic testing of the full structure only if the prototype is designed to have the dynamic simlitude with the full scale structure. In order is generate the same level of strains in the scaled model the accleration time history is scaled up.
you may refer this more details:
http://www.iitk.ac.in/nicee/wcee/article/13_3360.pdf
Please have a look at the similitude laws that link the prototype to the model. If gravity is taken into consideration in your model, then the scaling factor for time is the square root of the scaling factor for length. For example, if your scaling factor for length is 25, the time step of your earthquake is 5 times smaller.
the problem is that in the articles that interests me they don't talk about the scaling factor ! they directly put the results of the simulation using matlab and simulink ! and i can not know what is the scaling factor they use if a want to reproduce the same structure in the articles.
I suggest you contact the authors of those publications directly and ask them which scale they used. Good luck with your work.
Well I think reproducing the results should not be a problem as the values in M, K and C materices are already scaled. You need not bother about the scaling factors for them. Use them as it is. Just scale the acceleration time history. If you want to know the properties of the original structure refer [12,13] as they mentioned.
i already did that but I think that I have to scale the time and acceleration, about the time it is ok ! but about the ground acceleration how can I scale it down ?
It depends on how you want to scale the acceleration. If you scale the length (L) of your specimen by a factor S, and you want peak acceleration values to be the same (unscaled) for the prototype and the model, then you will find that you have to scale the time as follows.
Acceleration is proportional to L / T^2. Since the size of the specimen is scaled by S, then the earthquake displacement should also scale by S. Hence, in order for the acceleration scale to be 1.0, you need to scale time such that:
(Time Scale)^2 = (Length Scale).
Hence, (Time Scale) = sqrt(Length Scale) = Sqrt(S)
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