# Experimental Modal Analysis of Hand-Arm Vibration in Golf: Influence of Grip Strength
## 6 Discussion  
The works presented herein rely on experimental modal analyses, with the purpose of readjusting the numerical model and assessing the influence of grip force on the modal behavior of the shaft. The values of eigenfrequencies that were identified in standard boundary conditions (i.e., free and fixed) compare quite well to those found in the literature, even if the clubs are different [29; 30; 40]. [PERSON] [41] reports that skin is sensitive to vibrations up to 500 Hz, with enhanced sensitivity in the range 100-320 Hz. Subsequently, the participant may be sensitive to the first three modes in each plane. Modal analysis in the case of grip-free BCs highlights the limited influence of the grip force on the modal frequencies of the shaft, but a much greater one on damping. A mean difference of 1.02% is observed in frequencies, with a range of 0.00 to 4.22%. Regarding damping, the mean difference is 26.51% and it lies within the range \(-\)7.98-82.14%. The seventh mode is the most affected by the level of grip force, which corroborates the conclusions that are drawn in the scientific literature. The effect on modal damping is confirmed in the works by [PERSON] et al. [32] on tennis rackets and those by [PERSON] [42] on baseball bats and hockey sticks. These studies show that the damping values increase with the level of grip strength. However, broader variations are stated regarding eigenfrequencies: for instance, [PERSON] et al. [32] highlight a decrease of 15% (\(\pm\)5%) between the low and high levels of grip. The present paper concludes that the RMS value is minimal for a moderate grip force, which appears to be optimal in terms of performance and comfort, although not all users adhere to it. [PERSON] et al. [33] report that amateurs tend to exert a higher grip force on the shaft than professionals, particularly in the ascending phase of the shaft. Besides, the development of medial epicondylitis, which is favored by vibrations, turns out to be more frequent in amateur golfers (24%) than in professional or high-level amateur players (4%) [43; 44]. Hence, a correlation between the amateur population and vibratory dose may partly account for medial epicondylitis. \begin{table}
\begin{tabular}{c c c c} \hline
**Vibratory Doses** & **Strong Grip** & **Medium Grip** & **Weak Grip** \\ \hline \(a_{lnd}\) (m\(\cdot\)s\({}^{-2}\)) & 3.04 & 3.01 & 3.09 \\ \(a_{thrg}\) (m\(\cdot\)s\({}^{-2}\)) & 2.31 & 2.29 & 2.35 \\ \hline \end{tabular}
\end{table} 
Table 6: Weighted effective values of acceleration [3]. \begin{table}
\begin{tabular}{c c c c} \hline
**Grip Strength** & **T1 = [0,0.005] s** & **T2 = [0.010,0.015] s** & **T3 = [0.020,0.025] s** \\ \hline Strong & 183 & 119 & 39 \\ Medium & 151 & 120 & 36 \\ Weak & 182 & 123 & 56 \\ \hline \end{tabular}
\end{table} 
Table 5: Evolution of root mean square (RMS) value (m/s\({}^{2}\)) after contact. Based on the standards governing the calculation of vibratory doses, the present study shows that the right hand-arm system (for a right-handed player) is more exposed than the left system. A discrepancy below 1.3% exists between the vibratory doses for all three levels of grip strength, which enables us to conclude that it is not a determining factor in their decrease. However, the RMS value of acceleration varies by 23 m/s\({}^{2}\), depending on the grip force: in this regard, spectral content is key. For the three different intensities of grip strength, spectral analysis actually shows that 86% of the spectral content lies in the 95-110 Hz range, with the interval of interest being 0-400 Hz. Relying on the frequency weighting curve from standard ISO 5349-2, the 95-110 Hz range shall be given a 0.1 weighting factor, with this factor decreasing beyond 100 Hz. This calculation method justifies the small gap between the values of \(a_{\mathit{Hv}}\) in Table 5: the frequency weighting diminishes the amplitude of discrepancies. The results show that the limit duration is 5h22; however, a golfer is not submitted to continuous vibration during this duration per day.