## General Mechanical

#### Why does the mesh size affect my modal analysis results?

• Rameez_ul_Haq
Subscriber

The need for mesh refinement in a structural analysis module such as Static or Transient is quite clear; if we want the overall results such as displacement and stresses to be more accurate within the elements, then by refining the mesh size we should be able to achieve this. This happens because the mesh refinement improves the quality of the mesh elements and hence the shape functions (of each element) also becomes more accurate and closer to its ideal form, which in turn improves the accuracy of the results within the elements.

But for modal analysis, I couldn't understand the reason that why would inserting more mesh elements within my model would change the natural frequency results? I mean the purpose of modal analysis is not to acquire nodal displacements, neither obtain any elemental strain or stress results; displacements are random and strain/stress results don't exist since there is no force application at all. So why modal fequencies have dependence on the mesh size?

Below shows an example I just did to further elaborate my point.

• peteroznewman
Subscriber
You will find there is a small difference in stiffness between the 0.5 and 2 mm mesh size. Apply a 1 N tip force and show the difference in deformation between the two meshes.
• Rameez_ul_Haq
Subscriber
,fixed support at left end and 1 N force along =Z direction on right end. [Material = Aluminum Alloy, Large Deflection = OFF].
Well, yes. The deformations are different for both of these mesh sizes. So it means that the mesh size actually affects the stiffness of the body, and it just not depend on the unmeshed geometric dimensions of the body; infact mesh size plays a vital role here as well. Okay, so now I understand that the natural freqs would change if mesh size is changed, since overall stiffness of the body changes.
My basic concern was that why is this not an acceptable approximation to just idealize the complete body as a single point mass 'm' and then apply the relevant stiffness to it (calculated by hand), apply the support and then use analytical equation to find out the natural freq and mode shapes of it. But I think that this is not the greatest way to opt for; a single point mass could have 6 DOF's in total, so I would be able to only observe the deformation behavior or pattern of only the center of mass of the body at the respective mode and not of the complete body. By breaking the body into several mesh elements (which are infact all joined together by relevant stiffnesses), I would be able to observe the behavior of each of the nodes at that certain natural freq (which make up the complete body), and thus I am observing the overall behavior of the complete body at that natural freq.
The only question which remains now is that, okay, I mean I understand that the deformation behavior of the body can be observed by mode shapes at a certain natural freq from the modal analysis results, but assume I don't want to gain information about mode shape but only the natural freqs of my system. So in this case idealize the body as a single point mass (and then using analytical equations to calculate the natural freqs) would be an acceptable approach or not?
Plus, assume I conduct a modal analysis and I get first natural freq of, say, 10 Hz. We know that the total number of DOFÔÇÖs for a FEA model will result in as much natural freqs (and mode shapes). So the node associated with this natural freq of 10 Hz is supposed to have the highest amplitude (when behaving at the shape of the relevant mode) than all the other nodes when, say, is exicted by an external force of this much freq?

• peteroznewman
Subscriber
Some useful dynamic analysis can be done using a spring and point mass model, but few structures can be idealized where a spring and mass is a sufficiently accurate representation of the structure.
Fortunately, with solid models and automated meshing, a Modal analysis can be done quickly and the natural frequencies and mode shapes can be known.
• Rameez_ul_Haq
Subscriber
,can you kindly also write some of your views on the last paragraph of my last comment:
Plus, assume I conduct a modal analysis and I get first natural freq of, say, 10 Hz. We know that the total number of DOFÔÇÖs for a FEA model will result in as much natural freqs (and mode shapes). So the node associated with this natural freq of 10 Hz is supposed to have the highest amplitude (when behaving at the shape of the relevant mode) than all the other nodes when, say, is exicted by an external force of this much freq?
• peteroznewman
Subscriber
The paragraph doesn't say the purpose of the Modal analysis and it doesn't say if 10 Hz is above or below a requirement on the first natural frequency. Many structures have a minimum first natural frequency requirement.
The actual amplitude of the structure depends on the loads applied. Those loads might be applied in a Harmonic Response analysis, a Response Spectrum analysis, a Random Vibration analysis or a Transient Structural analysis. You should take a course in each of those to know when to use each one.
• Rameez_ul_Haq
Subscriber
,I mean yes I am aware that amplitudes or displacements depend on the load applied, and I already mentioned that in my original question, and the displacement results from modal analysis don't occur to be useful at all. And the displacements are just relative between each node for a certain mode shape in modal analysis.
I am currently taking courses to understand the link between natural freqs/mode shapes with FEA (like modal analysis). And yes, I would also continue with the rest of the modules which you have mentioned very soon.
• peteroznewman
Subscriber
While the Modal displacement amplitude is arbitrary, the shape is useful and the element strain energy is very useful to decide on the best place to add stiffness and the best place to remove mass to raise the first natural frequency.