# Free and Forced Vibration Modes of the Human Fingertip
## 6 Conclusions  
This study focuses on the dynamic analysis of a human fingertip through computational simulations. We developed an inhouse finite element analytical framework capable of generating 3D finger models and performing free and forced vibration analyses. The resulting finite element model of the fingertip, DigiTip, includes the details of six tissue layers (stratum comeum, epidermis, dermis, hypodermis, nail bed, and fingernail) and the characteristic profile of the distal phalanx, which is the bone supporting the fingertip. We performed modal analyses to determine the free vibration modes with associated frequencies below or around 250 Hz. Seven characteristic vibration patterns were found in the frequency range of interest. Next, we utilized frequency-response analyses to predict forced vibration responses of the fingertip excited by harmonic forces applied on a small patch of skin at the fingerprint centroid in three orthogonal directions. The forced vibration analyses revealed that certain free vibration modes tend to be excited significantly more efficiently than the others under these conditions. The results give valuable insight into the probable dynamic behavior of the fingertip in haptic applications involving vibratory feedback, and they show the usability of modal information in predicting the forced vibration responses of soft-tissue. In future studies, we plan to conduct experiments with human fingers to analyze the coherence between real measurements and our simulations. We hypothesize that some variations in tactile perceptual capabilities may be caused by differences in the physical structure and properties of the fingertip itself, as these clearly impact the fingertip's resonant modes. Consequently, the sensitivity of the results to changes in key model parameters (e.g., finger dimensions, elastic moduli of the tissue layers) will be investigated. We also aim to consider scenarios involving multiple excitations at different locations and examine internal strains around the mechanoreceptor locations. As previously demonstrated by [4] and others, we believe the simulated strains can be used as input for neural models to predict tactile responses of the skin subjected to dynamic forces. Figure 7: Forced vibration mode shapes of the fingertip excited by harmonic forces applied in the region of the fingerprint centroid. The loads are applied in the normal, radial–ulnar, and distal–proximal directions. The excitation frequencies range from 0 (static condition) to 250 Hz with an increment of 50 Hz. **Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/app11125709/s1](https://www.mdpi.com/article/10.3390/app11125709/s1)]([https://www.mdpi.com/article/10.3390/app11125709/s1](https://www.mdpi.com/article/10.3390/app11125709/s1)): **Video S1. ** An animation showing the first seven natural modes of the fingertip. One full cycle is shown for each mode, synchronized for comparison, even though their actual frequencies differ. **Video S2. ** An animation showing the forced vibration modes of the fingertip excited by dynamic forces with different directions and frequencies. One full cycle is shown for each mode, synchronized for comparison, even though their actual frequencies differ. Since the excitation amplitude is 0.1 N, the deformations are small but still observable on close inspection. **Author Contributions:** conceptualization, G.S. and K.J.K. ; formal analysis, G.S. ; investigation, G.S. ; methodology, G.S. and K.J.K. ; software, G.S. ; supervision, K.J.K. ; validation, G.S. ; visualization, G.S. and K.J.K. ; writing--original-draft preparation, G.S. and K.J.K. ; writing--review and editing, G.S. and K.J.K. Both authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. The article processing charge was covered by the Max Planck Digital Library. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.