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. Author manuscript; available in PMC: 2023 Apr 1.
Published in final edited form as: J Mech Behav Biomed Mater. 2022 Jan 29;128:105100. doi: 10.1016/j.jmbbm.2022.105100

Figure 4. Thin-plate theory for modeling the effects of foundational loading on wave dispersion.

Figure 4.

(a) The dispersion curves demonstrate a shifting of the frequency intercept as the foundational spring constant (Ka) is incremented from 0–7.7 × 104 N/m3 (where E = 3.0 × 104 Pa and σθ = 0 Pa). Only the low-frequency regions near the intercept are affected by the foundational loading and almost no change is seen at higher frequencies. (b) The corresponding phase velocity curves demonstrate an asymptotic behavior below approximately 1 kHz frequency which is a direct effect of the shifting frequency intercept. As the foundational spring constant increases, the vertical asymptote shifts to higher frequencies. This is compared to a system with no foundational loading (blue curve) where this asymptotic behavior is not seen.