Based on
the impulse formulation, we can derive the fundamental expression for the
impact load on a dynamic system. From here, we can produce Duhamel’s integral.
A system that experiences the impact load is often assumed as undamped system,
given the damping component may not have enough time to play its role in
resisting the load.
We first
look into the load case where the dynamic system is subjected to impact load of
fixed magnitude for indefinite timeframe. Under this situation, the general
equation for displacement response is obtained.
Then, for
the case where constant load is exerted for a limited duration of time, we need
to analyse it in two phases. It is noteworthy that the condition of system at
the end of the first phase shall be applied as the initial condition for the
second phase.
The following shows the derivation of solution for displacement response under impact load. Watch the video above for full details.
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