# Acoustics and Vibration Animations

Daniel A. Russell, Graduate Program in Acoustics, The Pennsylvania State University

Based on a work at http://www.acs.psu.edu/drussell/demos.html.

The content of this page was originally posted on May 24, 2019.

# Vibrational Analysis of a (cutlery) Fork

I have published three papers and couple of webpages about the vibration and radiation of sound from tuning forks. A couple of months ago, I found a simple looking fork when I was cleaning out my research lab space and I was curious to see if a cutlery fork would exhibit any vibrational modes where the tines moved in opposite or alternating directions.

## Modal Analysis

Experimental Modal Analysis is an experimental method that provides the vibrational mode shapes, their natural frequencies, and damping rates for a structure. A small (0.5g) accelerometer was attached underneath at the handle end of fork. A miniature impact force hammer was used to tap the fork at 1-cm intervals along the length of the fork. The ratio of acceleration to force (called the frequency response function) was recorded for each impact location. The collection of 57 frequency response functions was curve fit using STAR Modal software. The resulting relative amplitudes of motion corresponding to each measurement point were mapped to the grid point representation of the fork, resulting in shapes as shown below. The resulting shapes weren't as exciting as I had hoped - and I was not able to observe any modes below 25,600 Hz where the tines moved in opposite directions (at least for a freely supported fork). I guess I shouldn't have been surprised to discover that for forks behaves pretty much like a slightly non-uniform free-free beam.

The left photo shows the fork freely supported by rubber bands, with the accelerometer attached to the underside of the handle, and the miniature force hammer. The right photo shows the structure mesh grid in STAR Modal.

## Mode Shapes

The mode on the left is the first bending mode at 269 Hz. The mode on the right is the second bending mode at 744 Hz.

This second row shows two variations on the first torsional (twisting) mode, the one on the left at 1,940 Hz and the one on the right at 3,028 Hz (I need to double check this frequency).

This row shows the 5th bending mode at 4,300 Hz and the 3rd torsional mode at 10,165 Hz.