## 4 Results and Discussion
### Dynamic Mechanical Properties of Polyurea
#### 4.1.5 Effects of Excitation Amplitude  
The effects of varying excitation amplitudes (0.5 mm, 1 mm, and 2 mm) on the dynamic stiffness and damping characteristics of a \(\phi\)40 mm \(\times\) 20 mm polyurea sample under a constant 200 N preload at a 0.5 Hz excitation frequency were investigated. Figure 11 illustrates the force-displacement curves, along with the variations in dynamic stiffness and damping coefficient, under different excitation amplitudes.  
Figure 11: Effects of excitation amplitude on dynamic stiffness and damping coefficient: (**a**) force-displacement curves; (**b**) dynamic stiffness; (**c**) damping coefficients.  
Figure 10: Effects of excitation frequency on dynamic stiffness and damping coefficient: (**a**) force-displacement curves; (**b**) dynamic stiffness; (**c**) damping coefficients.  
Figure 11a demonstrates that the area enclosed by the force-displacement curve for the polyurea samples expands significantly with increasing excitation amplitude, reflecting enhanced energy dissipation capacity. Notably, the slope of the force-displacement curve remains nearly constant, indicating stable dynamic stiffness. Furthermore, although both damping and elastic restoring forces increase with excitation amplitude, the latter exhibits a more pronounced growth rate. As shown in Figure 11b,c, the excitation amplitude has a negligible effect on dynamic stiffness, which remains stable at approximately 81 N/mm, while the damping coefficient decreases from 268.19 N\(\cdot\)s/m to 209.67 N\(\cdot\)s/m with increasing amplitude. In practical applications where polyurea damping structures are arranged in parallel with metal lattice structures, the deformation of the lattice constrains the vibration displacement of the polyurea. When employed in vibration isolation systems, the metal lattice structure operates within its linear elastic regime, exhibiting relatively minor deformations. Consequently, during dynamic stiffness and damping characterization of polyurea materials, it is recommended to employ low-amplitude excitations.  
Previous studies have demonstrated that polyurea materials exhibit superior damping characteristics under dynamic loading. The dynamic stiffness and damping coefficient can be effectively modulated by adjusting the preload, area, and thickness. The systematic analysis of polyurea's dynamic stiffness and damping properties reveals that decreasing the material thickness can effectively enhance the damping coefficient. Nevertheless, this geometrical modification may induce a marginal elevation in natural frequency, attributable to the concomitant increase in dynamic stiffness. Thus, a balance must be struck between the natural frequency and response peak, depending on specific requirements. In this study, the polyurea specimen was fabricated with the dimension of 80 mm \(\times\) 40 mm. Under a pre-compression displacement of 6 mm, the estimated dynamic stiffness (\(k_{1}\)) and damping coefficient (\(c_{1}\)) are 80 N/mm and 200 N\(\cdot\)s/m, respectively. When the pre-compression displacement increases to 8 mm, \(k_{1}\) rises to 96 N/mm, accompanied by an increase in \(c_{1}\) to 300 N\(\cdot\)s/m.