In sports such tennis, the sound and vibration from the impact between racket and ball contribute to the ‘feel’ of a racket. Experimental Modal Analysis (EMA) is a technique that can be used to identify the natural frequencies, damping and mode shapes of an object, however, there are a number of challenges in applying this technique to lightweight, handheld sports equipment. Addition of measurement transducers can change the mass distribution of the racket whilst it is difficult to replicate the boundary condition of a hand-held racket in a controlled and repeatable manner. Jon’s research has focused on the use of non-contacting methods for measuring the vibration response of rackets and studying the effect of the human grip.
Aim
The aim of this project was to identify the modes associated with vibrations measured from a racket during normal tennis play
Approach
- Method developed for conducting a 3D modal analysis of a tennis racket using a laser vibrometer to measure vibration
- The effect of frame properties, string properties and string dampers on the natural frequencies and mode shapes of a strung racket studied
- Mass added to the grip to simulate a hand—held boundary condition
- Natural frequencies from EMA correlated with sound and vibration spectra from tennis shots
- Sound and vibration data correlated with players’ perceptions
Results
Key Findings
- 3D modal analysis identified frame bending modes, out-of-plane, in-plane, as well as torsional modes, hoop modes and stringbed modes
- Hand-gripping can be considered as a mass modification distributed along the handle of a freely suspended racket but the effective mass is much lower than that of an actual hand
- The hand also increased the damping ratio of frame modes significantly
- Dominant frequencies in the sound and vibration spectra from tennis shots could be correlated with the mode shapes identified
- String bed modes were found to excite the frame of the racket
Publications
- Banwell, G.H., Roberts, J.R., Halkon, B.J., Rothberg, S.J., Mohr, S. (2014) Understanding the Dynamic Behaviour of a Tennis Racket under Play Conditions, Experimental Mechanics, 54(4), pp.527-537.
- Banwell, G, Mohr, S, Rothberg, S, Roberts, J (2012) Using experimental modal analysis to validate a finite element model of a tennis racket. Procedia Engineering, 34, pp.688-693.
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