Discussion
Duhamel's integral cannot be applied directly to a structure that
Answer: A
Correct answer: behaves inelastically during the excitation
The integral superposes the responses to a sequence of impulses, and superposition holds only for a linear system.
Once yielding begins the stiffness depends on the displacement history, the response to two loads is no longer the sum of the responses to each, and the whole construction fails. Step-by-step numerical integration is used instead, updating the stiffness at each step. Multiple degrees of freedom and any damping ratio are handled comfortably; nonlinearity alone defeats it.
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