Hopefully I'll be able to clear up some misconceptions.
The dynamic shock method come from the days when hand calculations were used to estimate the response of a structure to a transient event (like a blast, impact, seismic event, etc). This type of analysis uses a Response Spectrum Curve (RSC) as an input. A RSC is a plot of the response of a single-degree-of-freedom (SDOF) system that is tuned to each frequency from some transient load. The big assumption was that your structure behaved like a SDOF. You would calculate the natural frequency of your structure and use this value to "look up" the response of your structure on the RSC, and then apply this value as a static load. For example, say you calculate your structure to have a fundamental mode of 8 Hz, and your RSC shows 1.1 g's at 8 Hz. You would then apply 1.1 g's (relative to some axis) as a static load and calculate the structure's response. Once numerical methods started becoming available, it became more viable to calculate multiple modes and apply the corresponding response to each mode. Using the previous structure as an example, say your first three modes at 8 Hz, 14 Hz, and 24 Hz. The RSC gives 1.1 g's, 0.9 g's, and 0.5 g's for the respective frequency values. You would then perform three separate linear static analysis and generate three separate responses. The question now becomes, "what is my total response?"
This is where the modal combination methods come into play. The simplest is the Absolute Sum (AS), where the absolute response values are directly summed together. As you can imagine, this can give fairly conservative (i.e. larger) results compared to what you might measure in a physical tests. The next method is the Square Root of the Sum of the Squares (SRSS), where each modal response is squared, summed up, then the square root is taken of the total value. This statistical method is usually more accurate than the AS, but a caveat is that you need to make sure each mode is "well spaced" (i.e. that spacing between each mode is large enough). There are other, more robust methods out there, such as the Complete Quadratic Combination (CQC), ROSE, and a navy method (I can't recall what it is called at the moment).
To perform a "dynamic shock" analysis, you must first perform a modal analysis to extract the eigenvectors/values for your structural. You then perform a dynamic shock analysis with whatever RSC you need to design to, and apply the appropriate modal combination method. Typically, you RSC is define in a standard. For example, if you need to design a structure to withstand a "Zone 4" earthquake, standards such as Telcordia's GR-63 define the RSC for a "Zone 4" earthquake.
Now, why do a dynamic shock analysis instead of a transient analysis? Well, a dynamic shock analysis uses linear superposition, so it's much faster compared to a fully transient (i.e. explicit dynamics) analysis. Furthermore, most of the computational work is done on the eigenvector/value extraction, so once you have your mode shapes and mode values, you can run different RSC without having to re-run the modal analysis. However, you need to ensure that what you're trying to model can be accurately represented with linear superposition theory. If not, then a transient method is needed.
