In our previous blog we explained what a Mode Shape is and why it is important. Now we will dive in to how you determine the number of mode shapes you need for an accurate and reliable analysis.
There are essentially two methods. The first one is to consider every node in your model. The number of Mode Shapes must be less than or equal to the number of unrestrained translational degrees of freedom per node.
- A planar structure (2D) has three degrees of freedom per node. Two translational in the X- and Y-direction as well as one rotational about the global Z-axis.
- A spatial structure (3D) has six degrees of freedom per node. Three translational and three rotational for all three of the global axes.
- This might not always be the case as a 2D truss has only two degrees of freedom and a 3D truss has three degrees of freedom per node.
This is all good and well, but with large models you have thousands of nodes. Having thousands of mode shapes is simply not feasible, nor necessary.
The last (and most applicable) method is to consider the Mass Participation Percentage. The more mode shapes you have, the higher the Mass Participation Percentage will be. There are guidelines for what an acceptable percentage will be and this ranges from >80%, some not accepting anything less than 90%. In SUMO, these values can be observed in the Grid View set to display Frequencies.
The total value for each of these columns needs to be above the prescribed percentage. Increasing the number of mode shapes increases the Mass Participation Percentage. Below you will note that 92 mode shapes were selected for the same model as above and that the Mass Participation Percentages have increased.
Determining the number of mode shapes by considering the Mass Percentage Participation is a simple and accurate method.
Still looking for answers? Start a discussion with other professionals in your industry!
