# Linear Transient Dynamic Analysis

## 19 Jun 2020 Linear Transient Dynamic Analysis

A linear transient dynamic analysis is performed if the variation of the load is very fast or, in other words, the period (https://www.fea-solutions.co.uk/frequency-and-period/) of the load variation is shorter than the first natural frequency (https://www.fea-solutions.co.uk/modal-analysis/) of the structure (https://www.fea-solutions.co.uk/static-vs-dynamic-analysis/), but if non-linear effects (https://www.fea-solutions.co.uk/non-linear-behaviour/) don’t have to be considered.

For a linear transient analysis, there are two methods used:

• Modal Superposition
• Direct Integration

For the Modal Superposition method, a modal analysis is performed first. The results from this are then used to apply the acceleration vs time spectrum for the transient analysis itself. This means the results of the final transient analysis are dependent on how many modes have been calculated in the modal analysis beforehand. For more information on Modal Superposition, please look at our blog: (https://www.fea-solutions.co.uk/modal-superposition/).

In the Direct Integration method, a modal analysis is not required. This is because the time integration is direct (and not a superposition). Therefore, the results of a linear transient dynamic analysis using direct integration will always be independent of any previous modal analysis, in particular independent of how many modes have been calculated, that means independent of the Cumulative Mass of the modal analysis (see: (https://www.fea-solutions.co.uk/modal-mass/)).

One of the many uses of a transient analysis is to calculate a system’s response to shock loading. Many codes for naval vessels are calling for linear transient dynamic analyses to qualify deck mounted equipment for shock loads, e.g. loads resulting from torpedo or mine explosions.

An example where a linear transient dynamic analysis is appropriate, would be stresses due to shock of a fabrication (welded structure), in this case a cabinet. The load is applied as ground acceleration versus time, typically with a period of 25ms, which equates to a frequency of 40Hz, which will excite the natural frequencies of the structure and an amplification of the load due to resonance (https://www.fea-solutions.co.uk/resonance/). As the cabinet is welded (hence no non-linear contact: (https://www.fea-solutions.co.uk/non-linear-contact/)) and plasticity (https://www.fea-solutions.co.uk/non-linear-material/) is not permitted, non-linearities will not have to be considered.

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