## 4 Our Current Work and Contributions
Matlab codes have been developed to calculate the vibration transmissibility ratios using the Range-Kutta numerical integration of the non-linear dynamic equation and using the Fourier transform and displacement frequency response function. The linear spring vibration isolator is also analyzed for the vibration transmissibility using the Fourier transform and displacement frequency response function. The double-diamond and linear spring isolator structures are also simulated through Adams simulation software where their models are shown in Figure 14.  
The transmissibility ratio for a conventional linear spring isolator element structure is calculated and plotted in the frequency range from 0.5 to 25 Hz, as shown by the dashed curve in Figure 15.  
It is seen from the solid and dashed curves in Figure 15 that the peak frequency and peak transmissibility ratio of the linear spring isolator structure supporting a mass model calculated by the analytical and ADAM simulation methods are the same where the peak natural resonant frequency is 13.78 Hz and the peak output response displacement amplitude is 66.54 dB (re 1 dimensionless). This result of ADAM simulation has verified the analytical model result, which means that both the analytical and ADAM simulation methods have been validated and can be applied to predict the transmissibility ratio of the double-diamond isolator structure, which will be illustrated below. The analytical and Matlab Simulink simulation results of vibration transmissibility ratios have been compared to the ADAMS simulation result for the double-diamond isolator structure supporting a mass model, which is given by Figure 16.  
It is seen from Figure 16 that the solid, dashed, and dot-dashed curves have very close peak frequencies and peak transmissibility ratios for the double-diamond isolator structure supporting a mass model calculated by the analytical and ADAM simulation methods where the peak natural  
Figure 14: Adams simulation for the double-diamond isolator element structure (**a**) and linear spring isolator element structure (**b**). Figure 15: Comparison of transmissibility ratios of the linear spring isolator structure supporting a mass model calculated using analytical method with Matlab code. resonant frequency is around 3.2 Hz and the peak displacement transmissibility ratio amplitude is \(-1.11\) dB (re 1 dimensionless). The analytical model has been validated by the ADAMS simulation result. It is seen from Figures 15 and 16 that the analytical results calculated from the Matlab codes have been verified by the results simulated from the Adams simulation software model for both the double-diamond and linear spring isolator structures. It has been confirmed that the peak transmissibility ratio of the double-diamond isolator structure is much lower than that of the linear spring isolator structure (peak value of 66.54 dB at 13.78 Hz for the linear spring-mass isolator and 1.11 dB at 3.2 Hz for the double-diamond isolator). Therefore, the double-diamond isolator structure is much better than the linear spring isolator for the peak transmissibility ratio and should be selected as the cell/unit/element structure of the 3D-printed seat cushion mattress. In the next stage, the geometric dimension and system parameters of the cell/unit/element structure of the 3D printed seat cushion mattress will be optimized for the lowest peak transmissibility ratio. The double-diamond isolator element structure will be cloned into multiple double-diamond isolator element structures to form a QZS or NPR seat cushion mattress that will be simulated using ADAMS or the ANSYS harmonic response module for its transmissibility performance. A prototype QZS or NPR seat cushion mattress will be designed and 3D-printed as test parts where the optimized double-diamond element structure will be selected for cells/units/elements of the 3D-printed prototype.