Response Spectrum Analysis

Response spectrum analysis is a combination of modal results scaled to match a given response spectrum. Extracting the modal results are static load cases means that the dynamic details are lost to the sub-model. To overcome this problem the response spectrum tasks are mapped to pseudo response spectrum tasks. A pseudo response spectrum task assumes that a static analysis case represents a mode shape. The dynamic details are supplied directly to the task in the form of frequency, modal mass, and effective masses. When a response spectrum task is extracted from the full model these details are recovered from the modal analysis and included in the pseudo response spectrum analysis task.

Given a shape from a pseudo modal analysis the scaling for each mode $i$, for excitation in the $j$ direction is:

$$u_{i} = \Gamma_{i,j}\frac{a_{spectral}}{\left( 2\pi f_{i} \right)_{2}}\phi_{i}$$

Where

$$\Gamma_{i,j} = \sqrt{\frac{\mu_{i,j}}{\widetilde{m}}}$$

If the pseudo modal analysis is carried out using the static procedure above, and the frequency and participation factor are known from the primary model, then the modal contribution to the response spectrum analysis can be estimated. Thereafter the combination is just as for any normal modal analysis.