Modal Analysis of a Tuning Fork

Tuning Forks are used to calibrate instruments and devices to a standard pitch. It finds application in tuning of music instruments, engineering devices such as MEMS Gyroscope etc. Each tuning fork is created with an unique frequency and are available commercially. For example, a tuning fork with Note A will have 440 Hz frequency, Note Cm has 261 Hz frequency etc.

Tuning Forks, when struck - vibrates in a complex motion pattern that can be mathematically called superposition of resonant modes. In this work, a tuning fork is designed to vibrate on a Note A frequency. It computes the fundamental eigenmodes and eigenfrequency of the tuning fork. A Tuning Fork was designed using SolidWorks and imported into COMSOL and its natural frequency was calculated. A Parametric Sweep for the Length 'L' of the cylinder is set up to search for the eigenfrequency range of 440 Hz and calculated. A series of lengths with corresponding eigenfrequencies are obtained, from which the desired length is chosen. The same problem is approached using the Shape Optimization Technique using the COMSOL BOBYQA Optimization Algorithm. The prong length is determined by nullifying the fundamental frequency with the target frequency value for a variable parameter set for Length 'L' in a specific range. The length of the prong cylinder computed agrees to the value computed by parametric sweep method.

Animation of the Tuning Fork Displacement upon vibrating at the Optimized Eigenfrequency of 440 Hz.

We observe the fork vibrating about a symmetry with negligible or no movement at the Handle. This means that the damping effect is minimum for the Design.