question regarding response acceleration vs excitation acceleration

[flyingcow1999a]

Based on the EOM, m*x_tt+c*x_t+k*x=f(t), if f(t) =m*a_g where the excitation acceleration a_g is the base/ground acceleration like earthquake loading, my understanding is that since the direction/sign of x and x_tt are unknown, the x_tt may be smaller/greater than a_g if x has the same/different direction/sign with x_tt.

I wanted to get a general idea of the relationships between x_tt and a_g.

Or can we say the response acceleration x_tt should MOSTLY smaller than a_g since k*x is positive and c*x is small/negligible. This is simple and straigthforward for a sdof system but I think the rule should be applicable to a mdof strucutre in which the a_g is allplied to all applicable dofs.

I observed x_tt > a_g for some dofs when I performed a time-history transient analysis for a building under earthquae loading (accelertion applied to all applicable dofs in the model). Can anybody discuss with me a little on what is in your mind? Thanks...

 

[GregLocock]

No it is very common for the response at a point on the structure to exceed that of the excitation point, in general. There is no hard and fast rule, but consider the vibration of the top deck of a skyscraper if you wiggle the foundation at the first resonant frequency of the tower.





Cheers

Greg Locock


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