Modal Superposition

Modal Superposition

All linear dynamic analyses https://www.fea-solutions.co.uk/types-of-dynamic-analyses/ except Modal Analysis https://www.fea-solutions.co.uk/modal-analysis/ use modal superposition. This is a mathematical procedure to use results from a Modal Analysis to calculate the effects of dynamic loads on a structure. In simple terms, modal superposition applies loads to the natural frequencies calculated earlier. That is why Modal Superposition is a type of restart analysis.

The results of a modal analysis are natural frequencies and their associated deformation shapes, whereas the results of the dynamic restart analyses, using modal superposition, are stresses and displacements. These results are therefore more indicative as to whether the system is safe or not.

Modal Superposition uses the free vibration normal mode shapes of a system. These are the patterns of motion that a system shows when vibrating at its natural frequency and can be called eigenmodes.

Modal Superposition uses these eigenmodes to uncouple the equations of motion which are in terms of the modal co-ordinates. Solving each equation independently will produce a solution for the modal co-ordinates. These co-ordinates are then used to find a solution to the original equations by superposition.

Modal Superposition is most useful when the frequency range of the loads applied is fairly limited, such as in a Harmonic Analysis. However, it is also very useful when doing dynamic analysis in the frequency domain, as all load frequencies are known beforehand.

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