Welcome to Today's Presentation: From Shaky Ground to Solid Analytical Decisions

Welcome everybody to today's presentation. From shaky ground to solid analytical decisions. Our topics today will relate to linear dynamics using ANSYS Mechanical. Besides myself, I'm Patrick Tessaro. I have Adrian Caudillo and Cameron Canter presenting with me today. OZEN Engineering.

We are experts at simulations of structural, thermal, fluid, and electromagnetic fields.

We are an ANSYS Elite channel partner and have been named America's Channel Partner of the Year by ANSYS in 2015, 2018, and 2021. We offer customers best-in-class software tools, consulting, training, mentorship, and technical support.

Today we're going to discuss and try to understand some of the strengths associated with modal analysis, harmonic analysis, response spectrum, and random vibration. Hopefully we're going to gather some insights towards producing high-quality results.

I'm going to begin the discussion on modal analysis. And of course, my colleagues may mute you as you come in, which is perfectly fine. Don't be distracted by that. Why perform a modal analysis? Our goal with that is to learn the mode shapes and natural frequencies.

We do this typically as preparation for a different dynamic restart analysis, such as harmonic response spectrum, random vibration, or a transient structural using modal superposition.

Also, from the modal analysis results, we can derive the appropriate time step size and analysis duration that might be used for a transient structural analysis using the direct integration method. What is a modal analysis?

The first step, it's the first step to learning and understanding the dynamics associated with geometry and applied loads. We predict the geometry's propensity to bend in ways that would otherwise be invisible. This propensity is exposed under dynamic loading.

And the dynamic analysis results depend on subsequent linear dynamic analyses to fully describe the dynamic response. I'm going to do some demonstration, learn how the software works in a very high-level way.

My aim is to set some controls for the analysis so that our results are readily available for subsequent analyses. We're going to look at modal stress and how it can be useful to us. And this concept of modal effective mass. Let's take a look and see what we have.

So first, I think it'd be important to understand how do we get started with modal analysis. We do this by a drag-and-drop method. We can simply double click or drag our modal analysis onto the canvas. And from there, we could load our geometry and begin editing the model within ANSYS Mechanics.

And from there, we could load our geometry and begin editing the model within ANSYS Mechanics. I've already set something up so that we're already on our way. I brought in a very simple geometry and I've generated a simple mesh on it as well. I'm going to select a surface and fix that.

You don't have to add a fixity on your geometry. But our goal is to replicate how this geometry is going to be applied to the model. And we're going to demonstrate how this geometry will be constrained when it's in use.

So in my case, I've got this rectangular rod sticking from the wall for some reason. And we're going to learn a little bit more about this. Within the analysis settings, there's some things that we want to take a look at.

If I, from within ANSYS Mechanical, was going to initiate another analysis type, I might want to activate the model. I might want to activate the future analysis option here. And I'd say that I'm going to perform a modal superposition analysis to follow that.

And make some other changes so that all the right results are available and I don't have to rerun my analysis if I added another analysis type after this. On the output controls, I could see that stress is included and that's fantastic. By default, it's not. I have enough.

Let me go ahead and run my analysis. By default, our settings are such that it will solve for the first six mode shapes and there would be reasons why I'd want to request more.

I can select all of these and create the modal results and then evaluate all these and then I can see how my model would demonstrate a vibration. I can also see the vibration mode and at what frequency that would occur. Animating a couple of these allows me to see what kinds of shapes exist.

But this is only part of what I'm interested in. The other thing that I'm looking for is, let me insert a stress. So I'm going to insert an equivalent stress and I'll define that to act on motion. I'm going to name this mode shape number three. Let's evaluate this result.

What I see here on my model is areas where stresses would be a peak if this mode shape were excited. Now, I don't really, I'm not really interested in the value of the stress because at this point, it falls into the category of meaningless. But the location on this model is very important.

I'm going to go ahead and add a stress. And I'm going to say that I want to add a stress. So I'm going to add a stress or less than less value to loading's US China based on this location. So then I hit space plus one extra layer plus a fixed value.

Then again, I am going to add a stress to this model only because my model has a lot of stress at its physical site dimensions. My body sim ed to add a stress, between change our solution output to look at participation factor summary. We scroll to the bottom.

This is where we could see highlighted in yellow the sum of all the mode shapes' participation in an accumulation of modal effective mass. 80% it reads for the x direction, y direction, z direction.

This is important because if I plan to perform a subsequent analysis based on these mode shapes, I will want to hopefully consider enough modal effective mass such that if I included additional frequencies, my results would not change. But this is only part of the story.

What if we looked at our geometry and we included additional components? Let's take a look at the geometry. Here we have the same geometry, except we have an additional plate behind it. And this plate is fixed on its back end. So in essence, I get the same mode shapes that I had before.

Slightly different, but very much the same. Here's the big point. We look at the solution information. We scroll down and when we look at the modal effective mass, now we see that it's 10% in the x, y, and z directions. Let's see why that is. Go back to presenter mode.

So between the two models, the mass of our rod is the same. But the fixed plate adds a lot of mass to the entire model. When we list the modal effective mass in our summary, we're doing so based on the entire geometry.

Even though the geometry is the same, even though the entirety of this plate is fixed, it still contributes to this calculation. So it could be a little misleading, depending on the geometry and the kinds of boundary conditions we have.

When we calculate to determine how much of this beam's mass is vibrating, we could see what it is, 27 kilograms.

And if we considered that same amount of vibrating mass, just considering the volume of this rod, we could see that we get about the same participation factor if we factor out our non-vibrating mass. So in summary, we want to set up our model. We're doing a linear analysis.

That means that our properties, our material properties are linear. They don't change. And also, the constraints don't change. We may consider pre-stress conditions. And this would be important if we thought that any pre-stressing would change the natural frequencies of our model.

Think about string instruments. That's a perfect example. We can consider damping. Damping could be either not entered. It could be defined as a material property. It could be a percent of global. And it could be mass and stiffness based Rayleigh energy dissipation damping.

The important results are mode shape, natural frequency. We talked about modal effective mass. We saw how modal stress can be useful for mesh refinement. And then behind the scenes, we have participation factor for subsequent analyses.

At this point, I'm going to hand it off to Adrian for discussion on harmonic analysis. Thank you.