The motion of the NDOF system in an earthquake includes the motion at the base, which we will take as a prescribed motion. In essence, we assume that the ground motion just happens to the structure and that the structure does not influence the ground motion (which is not completely true, but it is a good place to start with the problem). In this chapter, we add earthquake ground motions as a source of excitation, show how they impart dynamic forces in the shear building, and analyze the response those forces induce.
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The letter a gets a pretty hard workout in this book. In this case a i(t) is a continuous function of time, not a discrete acceleration. The subscript i indexes the mode number, not a time step number (which we usually designate with the letter n).
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Hjelmstad, K.D. (2022). Earthquake Response of NDOF Systems. In: Fundamentals of Structural Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-89944-8_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-89943-1
Online ISBN: 978-3-030-89944-8