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A simple frame structure was loaded with an AirZooka air cannon. The acceleration response was measured at the top floor with an iPhone 13 Pro running the Vibration Analysis app.
The lumped mass of the structure, including the phone, is 2.22 lb. The stiffness of the structure is 2.68 lb/in, resulting in a natural frequency of 3.44 Hz, or a natural period of 0.291 seconds.
We could develop the analytical model for the structure based on its geometric and material properties using stiffness and natural frequency formulas, but we will save this for later.
How much force can an AirZooka vortex cannon supply? Let's use our well-described structure and Newmark's Method to find out!
The response of the structure is plotted in the spreadsheet below. Open the spreadsheet and enter loading values in the orange cells in the p(t) column to attempt to align the measured and calculated responses.
A Hint
A Hint
Think about how much force a puff of air would impose on your face. It's small...right around 1 pound and is fleeting. If you start with -1lb for one of the 0.1-second intervals of p(t) you will be close!
Another Hint
Another Hint
Consider that the initial acceleration response is negative, so the loading should be negative.
The Answer
The Answer
At t = 0.12 sec, p = -0.9 lb, and at t = 0.13 sec, p = -0.7 lb. This results in a calculated peak acceleration response of -155 in/sec2 compared to a measured value of -154 in/sec2.
No consideration of blast loads is complete without pondering the forces generated by a nuclear blast. Indiana Jones offers some insight:
This excellent article at Structures Mag provides additional insight into the nature of blast loads and how we simplify the loading models to perform structural design for blast loads. Want to go deeper? Try this 2013 report by Varlos and Solomos: Calculation of Blast Loads for Application to Structural Components.
Resources
Resources
See my paper on the implementation of this activity in a structural dynamics course.
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