Applying intuition to Fourier analysis by rendering images with vibration
Tre DiPassio · The Journal of the Acoustical Society of America · 2024
It has been said that “Everything in life is vibration.” While this may seem dramatic, it is true that we can describe any shape as a superposition of a structure’s bending modes using Fourier decomposition. In this session, I present an assignment that involves the rendering of images and artwork using only a subset of a rectangular membrane’s mode shapes. This assignment allows students to engage with fundamental concepts such as Fourier analysis and the modal nature of structural vibrations in a way that allows them to see and interact with the results of their work. A natural extension is to simulate the response of a plate to an external stimulus using the Fourier series, and to verify the results of their simulation experimentally using tools such as laser vibrometry. While exciting complex patterns in the vibrational response of a real plate is difficult in practice, this assignment provides a memorable and engaging baseline for understanding the modal composition of induced structural vibrations.