## 4 Numerical Result
### Flutter Suppression
The influences of the displacement feedback gain \(K_{d}\) on the response of GPLs reinforced composite plate were considered when the Mach number \(M_{a}=3.08\) was less than  
Figure 8: The eigenvalues of the GPLs plate bond with a piezoelectric patch with respect to the Mach number under displacement feedback control \(\left(K_{d}=0,\ K_{d}=1.5\times 10^{5},\ K_{d}=3\times 10^{5}\right)\), **(a)** the real parts of the eigenvalues; **(b)** the imaginary parts of the eigenvalues. Figure 7: Response of the plate at the critical flutter number. the critical Mach number. Figure 9 shows the plate's response before and after displacement feedback control was introduced. It illustrates that the response of the GPLs plate will reduce more rapidly after applying the displacement feedback control. Figure 10 compares the GPLs plate's response before and after introducing the displacement feedback control at the critical flutter point \(M_{a}=3.09\). The response of the plate change from divergence to convergence, which means introducing the displacement feedback control can efficiently suppress the occurrence of flutter at the critical Mach number. The influences of the active mass \(\mathbf{M_{p}}\) produced by the acceleration feedback control \(K_{a}\) on the aeroelastic flutter properties of the GPLs plate with piezoelectric patch are addressed in Figure 11. Three cases of different acceleration feedback gain \(K_{a}\) were considered; \((K_{a}=K_{d}=0)\), \((K_{a}=0.3\), \(K_{d}=0)\), and \((K_{a}=0.5\), \(K_{d}=0)\). Similar to the displacement feedback gain \(K_{d}\), the acceleration feedback gain \(K_{a}\) can also su  
Figure 10: The comparison of the plate’s response after introducing the displacement feedback gain \(K_{d}\) control at the critical flutter point. Figure 9: The comparison of the response of the plate after introducing the displacement feedback gain \(K_{d}\) before the critical flutter point. critical Mach number of the GPLs plate from \(M_{a}=3.1\) to \(M_{a}=4.0\). The result implies that the acceleration feedback gain \(K_{a}\) could improve the aeroelastic characteristics of the GPLs plate. Figure 12 demonstrates the influence of the acceleration feedback control on the response of the GPLs plate before the critical flutter point. It illustrates that the acceleration feedback control leads to a faster decrement of the plate's response than that without the acceleration feedback control. Figure 13 reveals the comparison of the response of the plate before and after introducing the acceleration feedback control at the critical flutter point. It presents that the response of the plate will decay to zero after inducing acceleration feedback control instead of increasing with time for the plate without the acceleration feedback control. The results of Figures 11-13 indicate that adding an active mass \(\mathbf{M}\mathbf{p}\) to the GPLs reinforced composite  
Figure 11: The eigenvalues of the GPLs plate bond with piezoelectric layer with the Mach number under the acceleration feedback control (\(K_{a}=0\), \(K_{a}=0.3\), \(K_{a}=0.5\)) (**a**) the real parts of the eigenvalues; (**b**) the imaginary parts of the eigenvalues. Figure 12: The comparison of the response of the GPLs plate after introducing the acceleration feedback control before the critical flutter point for \(K_{a}=0.5\). plate through acceleration feedback control can also effectively enhance the aeroelastic flutter characteristics of the GPLs plate and suppress the response of the plate. Furthermore, the combination effect of displacement feedback control \(K_{d}\) and acceleration feedback control \(K_{a}\) on aeroelastic flutter characteristics was demonstrated in Figure 6:0 Three cases of the feedback gain (\(K_{a}=0.5,\ K_{d}=0\)), (\(K_{a}=0\), \(K_{d}=3\times 10^{5}\)), and (\(K_{a}=0.5,\ K_{d}=3\times 10^{5}\)) are considered.