# Forced Dynamics of Elastically Connected Nano-Plates and Nano-Shells in Winkler-Type Elastic Medium
## 8 Results and Discussion
### Forced Vibration of the ECSNPS
The influence of the radius of curvature \(R_{2}\), for \(R_{1}=\infty\), on the transverse displacement of the forced vibration for the first three modes of the ECSNPS is presented in Figure 5. The values of the radius of curvature R\({}_{2}\) vary from 150 to 850, while the radius of curvature R\({}_{1}\) tends to infinity. Lower values of the radius of curvature R\({}_{2}\) lead to a decrease in the amplitude of forced vibrations in both the nanoplate and nano-shell of the ECSNPS. Notably, the amplitude of forced vibrations in the nano-shell significantly decreases as the radius of curvature decreases, as illustrated in Figure 5b. It can be observed that as the radii of curvature decrease, the transverse displacement of the forced vibration for both the upper nanoplate and lower nano-shell of the ECSNPS also decreases. The effect of the one-sided and double-sided curved nano-shells on the transverse displacement for the first three modes of the ECSNPS is presented in Figure 6. The doubly  
Figure 4: Comparison of the amplitude values of the forced vibrations of the ECSNPS and the ECSTNP: (**a**) the upper nanoplate of the ECSNPS with the upper nanoplate of the ECSTNP; (**b**) the lower nano-shell of the ECSNPS with the lower nanoplate of the ECSTNP. Figure 5: Effect of the radius of curvature R\({}_{2}\) on the transverse displacement for the first three modes of the ECSNPS: (**a**) nanoplate; (**b**) nano-shell. curved shallow nano-shell has radii of curvature of \(R_{1}=150\) and\(R_{2}=150\) nm, while the one-sided-curved nano-shell has radii of curvature of \(R_{1}=\infty\) and \(R_{2}=150\) nm. The transverse displacement of one-side-curved nano-shell is marked in blue, while the transverse displacement of the double-sided-curved nano-shell of the ECSNPS is marked in gray. From Figure 6a, it can be seen that the vibration amplitude of the nanoplate is smaller in the ECSNPS with a one-sided-curved nano-shell. Figure 6b also shows that the amplitude of the forced vibration for the nano-shell of the ECSNPS is smaller with the one-sided-curved nano-shell. The conclusion is that the amplitude of the forced vibration is smaller for both the nanoplate and the nano-shell for the ECSNPS with the one-sided-curved nano-shell. The effect of the external excitation on the transverse displacement for the first three modes of the ECSNPS is presented in Figure 7. The following magnitude values of the uniformly distributed surface harmonic loads are used: \(\mathrm{F}_{0}=10\) nN, \(50\) nN, and \(100\) nN. It is observed that increasing the magnitude values of the external load increases the vibration amplitude of both the nanoplate and nano-shell of the ECSNPS. The effect of the nonlocal parameter on the transverse displacement for the first three modes of the ECSNPS is presented in Figure 8. The transverse displacements for the nanoplate of the ECSNPS are shown in Figure 8a, while those for the nano-shell of the ECSNPS are shown in Figure 8b. It is observed that the vibration amplitude of the nanoplate in the ECSNPS decreases with an increase in the nonlocal parameter, as seen in Figure 8a. Conversely, the amplitude of the forced vibration of the nano-shell in the ECSNPS increases  
Figure 6: Effect of the one-sided- and double-sided-curved nano-shell on the transverse displacement for the first three modes of the ECSNPS: (**a**) nanoplate; (**b**) nano-shell. Figure 4.0 Effect of the external excitation on the transverse displacement for the first three modes of the ECSNPS: (**a**) nanoplate; (**b**) nano-shell. with an increase in the nonlocal parameter, as shown in Figure 8b. Similar observations regarding the effect of the nonlocal parameter on a doubly curved nano-shell are also noted in [20]. The effect of the damping proportional coefficients on the transverse displacement for the first three modes of the ECSNPS is presented in Figure 4.1 It can be observed that an increase in the damping proportionality coefficients decreases the amplitude of transverse vibrations in both nano-elements of the ECSNPS.