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The displacement history of one story structure is known due to an unknown ground motion. The dynamic properties, such as mass and lateral stiffness, are known, and dimensions were also given. How to get the excited ground motion to the structure cause the displacement history?

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  • $\begingroup$ Could you be more specific with temporal resolution of the history and number of parameters that have been tracked? $\endgroup$ Commented Mar 12, 2023 at 12:23

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DISCLAIMER:This personal intuition rather than actual documented knowledge.

In most situations, I don't think you can infer it with certainty. I.e. it is possible for many different excitations to provide the same displacement history for a node.

The more information you have (i.e. time histories of nodes) the more constraints are applied. However, at the end of the day you are still looking at structure which is represented as a matrix $K$ and you have excitations $F$ and node displacements $u$, i.e.:

$$\vec{F} = \mathbf{[K]} \cdot \vec{u}$$

For this example, it is possible to have the vectors $\begin{bmatrix}1\\0\end{bmatrix}$ and $\begin{bmatrix}0\\1\end{bmatrix}$ multiplied by $\begin{bmatrix}1,0\\1,0\end{bmatrix}$ and still get the same result.

So --IMO-- the relation between displacement history and excitations would not be one-to-one.

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