## 3 Results
### Parametric Study  
Figure 5 illustrates the impact of the mass ratio \(\mu\) on both the vibration attenuation and energy harvesting performances of the ERS-TQZS VI system.  
Figure 6 illustrates force transmissibility and output power curves under different damping ratios \(\zeta_{1}\). We can observe from Figure 6a that the resonance peak decreases by 24.2% and that the resonance frequency decreases by 7.9% with a damping ratio increase from 0.01 to 0.1. The results indicate that a higher \(\zeta_{1}\) contributes to improved performance in attenuating low-frequency vibrations. From the perspective of energy harvesting, we can observe that the maximum output power at the resonant frequency decreases by 76.6% as \(\zeta_{1}\) increases from 0.01 to 0.1. Moreover, the influence of \(\zeta_{1}\) on the frequency range of energy harvesting can be considered negligible.  
Figure 7 shows the force transmissibility and output power curves of the ERS-TQZS VI system under different excitation amplitudes \(\widetilde{F}_{\epsilon}\) and also provides a comparison to the linearized system without ERSD. From Figure 7a, we can observe that the excitation amplitude has nearly no effect on the resonance peak of the ERS-TQZS VI system. However, the resonance frequency increases by 23.7% as \(\widetilde{F}_{\epsilon}\) increases from 0.001 to 0.01, leading to a degradation in the performance of low-frequency vibration attenuation. Conversely, from an energy harvesting standpoint, Figure 7b demonstrates a substantial increase in the maximum output power at the resonant frequency with the increases in \(\widetilde{F}_{\epsilon}\) from 0.001 to 0.01.  
Figure 5: The force transmissibility and output power curves of ERS-TQZS VI system under different mass ratio \(\mu\) (\(\zeta_{1}=\zeta_{2}=0.05,\widetilde{F}_{\epsilon}=0.005\), \(l=0.8\), \(\widetilde{C}_{d}=0.025\), \(\widetilde{C}_{\epsilon}=50\), \(\widetilde{R}=14\), \(\widetilde{C}=1\)): (**a**) the force transmissibility; (**b**) the output power.  
Figure 8 illustrates the influence of the shunt resistor \(\widehat{R}\) on both the vibration attenuation and energy harvesting performances of the ERS-TQZS VI system. From Figure 8a, we can observe that the resonance frequency of the ERS-TQZS VI system increases by 15.1%. Meanwhile, the resonance peak increases by 32.8% as the shunt resistor increases from 1.0 to 18.0. The results indicate that a smaller shunt resistor is advantageous for a better performance of low-frequency vibration attenuation. Therefore, as small of a shunt resistor as possible should be selected under the practical limitation of the ERS-TQZS VI. For energy harvesting performance, we can observe from Figure 8b that the resonant frequency at the maximum output power increases by 15.3% with the shunt resistor's increase. However, the shunt resistor nearly has no influence on the resonance peak of the ERS-TQZS VI system.  
Figure 6: The force transmissibility and output power curves of ERS-TQZS VI system under different damping ratio \(\zeta_{1}\) (\(\zeta_{2}=0.05\), \(\mu=0.2\), \(\widehat{F}_{e}=0.005\), \(l=0.8\), \(\widehat{C}_{d}=0.025\), \(\widehat{C}_{e}=50\), \(\widehat{R}=14\), \(\widehat{C}=1\)): **(a)** the force transmissibility; **(b)** the output power.  
Figure 9 illustrates the influence of the shunt capacitor \(\widehat{C}_{e}\) on both the vibration attenuation and energy harvesting the performances of the ERS-TQZS VI system. From Figure 9, we can observe that the force transmissibility and output power curves of the ERS-TQZS VI system remain almost unchanged with the increase in shunt capacitance. Hence, the impact of the shunt capacitor on the performance of energy harvesting and vibration attenuation can be neglected.