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FEA Vibration 201: Shock and Awe
The majority of simulation work I do now is with fluid flow and heat transfer using Computational Fluid Dynamics (CFD). However, my career was first launched doing structural analysis with Finite Element Analysis (FEA). I am old enough that my first FEA programs in college were written in Fortran and performed using batch computing.
An advanced aspect of FEA, more complex than linear static stress analysis, is that of vibration analysis. Vibration occurs in many common applications including automotive, aerospace and industrial machinery along with seismic considerations for building design.
Sometimes, it is found to be the culprit in unlikely situations. I recall an interesting read about an issue that an automotive OEM was having. They were shipping batches of new cars from Detroit to California by train, and upon arrival, all the batteries were dead. Of course, the first thing they investigated were the batteries and the electrical system, but they could not find the smoking gun. Finally, some bright engineer determined the cause. These new cars had a revised horn mechanism with a different spring rate. Along a certain stretch of track, the vibration from the train matched the frequency of the spring (known as resonance) and all the horns were blaring until the batteries died. The solution? Put in a spring with a slightly different rate to change its fundamental frequency.
There are a variety of vibration analysis types available, including time history, response spectrum, frequency response and random vibration. The starting point is a modal analysis, which extracts the natural frequency values and modes shapes of the structure in question. From there, the solver selection depends on the nature of the excitation inputs along with the type of results output which is desired. For example, random vibration is often used in the transportation industry because of the “randomness” of the input excitation profiles, and its output is in terms of probability.
Another popular vibration option is response spectrum, which provides the estimated system response while avoiding the complexity and computational expense of running it directly as a time history analysis and extracting the transient response. To achieve this, the transient input data is converted into a response spectrum.
Figure 1: Shock response spectrum for a 50g half-sine impulse loading with a 0.011 time base and 10% damping.
The following validation report for a response spectrum analysis provides details on the inputs and results for a simple structure subjected to a half-sine impulse loading.