## 3 Results and Discussion
### Shock Impact Testing  
The lattice structures responded significantly with well-controlled pressure between 1 bar and 4 bars, equivalent to the force between 200 N and 320 N. According to Equation (1), the shock data in volts (V\({}_{s}\), V) were converted into acceleration (a, g) and then treated by a bandpass filter from MATLAB(r) 2019b with a manually adjusted baseline correction. The results from the impact testing adjusted the baseline, using a band-pass Butterworth filter with a fourth-order filter at 500 Hz. To avoid signal aliasing, the sampling rate was 512 kS-s\({}^{-1}\), and the results of an impact in acceleration (a, g) obtained from Equation1 were converted to force and impulse by Equation (3). The reference force is an experiment that can be performed by using the impact without installing any sample on the fingers of the test rig. It can be seen that the acceleration and force were narrow-based and had an extreme shape, with a shock at high frequency. The shock (force) was not only used as the reference input force but can also be used as the representative of a non-isolation system. The first lattice structure is cubic perimeter (see Figure 9); under the impact force in cases (a)-(c). The acceleration results in \"g\" were 29.1 \(\pm\) 0.9 g, 37.5 \(\pm\) 0.1 g and 43.5 \(\pm\) 0.1 g, respectively. This series of responses showed the convolution of the response signal or dispersion of the unmatching frequency, caused by two or more transverse waves travelling at different speeds. This dispersion effect of the force would be a benefit for using as in impact isolation with a low transmutability (T, [-]). However, it has a limitation as it can only take a compressive force of less than or equal to 289 \(\pm\) 24 N.  
Figure 8: The plots of the empirical model are curve-fitting according to the Gibson-Ashby model and linear model (i) relative stress and (ii) relative elastic modulus. As mentioned earlier, the suggestion of using a cubic perimeter (CP) as the reference may rise in a quasi-static compression because this structure collapsed sequentially at the low strain rate, but under the shock acceleration, it could perform differently. The test results from this CP structure showed a sign of bending-dominated under all impulse input forces, especially at the higher impulse force. Under the quasi-static test, this structure did collapsed sequentially layer-by-layer but under a shock load, it was broken with a bending-dominated specimen. The series of impressions shown in Figure 10, from the beginning (i) to the end (iv); show the specimen was bending after impact (Figure 10 iii). This phenomenon may be negative compared with a collapsing mode during the quasi-static part of the experiment. Therefore the series of specimens: CP, BCC, FCC, BCC + CP, FCC + CP and solid, was subjected to the four levels of shock impulse forces. The primary responses were the plots of unsteady acceleration (**a**, g) and impulse time (\(\tau\), ms). This impulse time can be estimated by an (Equation 4). Despite a sine function, the half-sine plot has another form in a cosine function that would be more convenient to use than a function of sine. The inversion of a response impulse multiplied by two is a response frequency (f, Hz). Figure 11 shows the half-sine model plots against the experiment data under the excited force between 186 \(\pm\) 19 N and 308 \(\pm\) 11 N. It can be seen that the response impulse time was at a little lower level of excited force; hence, the higher the excited force is applied on the lattice structure, the higher response frequency would be, because of its impulse time reducing by 25 per cent between 186 \(\pm\) 19 N and 308 \(\pm\) 11 N.  
Figure 10: A series of impressions on the Cubic Perimeter (CP) under the shock excited force of 245 \(\pm\) 11 N: (**i**) initial (**ii**) begin collision (**iii**) exhibited significant bending deformation (**iv**) end.