Vibration is one of the key factors in engineering design that is so important to consider when designing components that see that type of loading. As I'm sure you all well know, every structure has its own natural (resonant) frequencies that correspond to a particular motion (mode shape) of the structure. The majority of the time, designers want to avoid operating their components at these frequencies in order to prevent disaster...wouldn't want another "Galloping Gertie" on our hands!

Much of this design work now-a-days is done through the use of simulation software like SolidWorks Simulation; SolidWorks' professional simulation package offers you this ability. Using the finite element method, the software breaks down the model of your design into small elements which can efficiently be used to solve your problems. No matter whether you are using SolidWorks Simulation or another simulation tool, the software is only as good as the person using it; this is why we stress so much the importance of getting training, particularly in the simulation area. Over the past few months I've tried to pick out some areas of our simulation package that people commonly use and do a justification study with them. There are a couple reasons I've done this. First, I want our customers to have confidence in the software they use on a daily basis. It amazes me sometimes all that this software can do. It's easy to get lost in that and forget that there really is a systematic method to how our results are achieved. Secondly, I want to help our customers in their design process by reminding them of some of the governing equations involved in solving these simulation problems so they can get the most out of the software.

I've decided this time to take a look at a simple vibration problem. Most of the systems we work with can be modeled as spring/mass systems. This example will show the process that most simulation software uses when solving for resonant frequencies and mode shapes. Below is the simple 2 degree of freedom system that we'll be working with.

We will start by simply modelling this system as two blocks; the first being twice the mass of the second. Within SolidWorks Simulation, we will use a spring connector to model the stiffness between the two masses and an elastic support for the connection to the fixed wall. Along with this, we will restrain the motion of the system to be only two dimensional.

Before we get into the results of this example, take a look at the hand calculation for this problem here. The process used in the hand calculation is the same process that SolidWorks uses to find the natural modes and frequencies of your vibration problems. The only difference is how the software solves the characteristic equation that I’ve shown in the attached document. When problems become much bigger, exact solutions are not known so iterative numerical methods must be used.

After running the study in SolidWorks Simulation, we see results that match our hand calculations. The first resonant frequency is *2.449 radians/second *and the first mode shape shows the second mass displacing twice that of the first. It is important to understand that these displacement values are only relative to each other and don't signify absolute displacements.

Similar to the first mode shape, the second mode shape also agrees with our hand calculation. The second mode has a frequency of *4.89 radians/second,* and the masses displace opposite of each.

Whether you use SolidWorks to run your simulation analysis or another software, the math behind these things is pretty much the same no matter what you are using; it's been around for a long time. The differentiator between simulation software is how easy a company makes it to use. SolidWorks has done this so well that it isn't required that you know the intricacies of what is going on behind the scenes. I find it interesting though sometimes to look under the hood and see all that SolidWorks does for us!

For More on SolidWorks Simulation, click to read Behind the Software with Beam Elements