## 4 Results and Discussion
Furthermore, the value of the dimensionless resonance vibration amplitude at postbuckling state is larger than those at prebuckling state when the same excitation is applied. Figure 7: Dimensionless amplitude-excitation frequency curves for different axial load at prebuckling state (\(P\leq P_{cr}\), \(m_{s}=0\), \(R=1k\Omega\), \(\kappa_{0}=0\) for distribution 1). Figure 8: Dimensionless root mean square voltage output-excitation frequency curves for different axial loads at prebuckling state (\(P\leq P_{cr}\), \(m_{s}=0\), \(R=1k\Omega\), \(W_{0}=0.01h_{t},\kappa_{0}=0\) for distribution 1). Figure 9: Dimensionless vibration amplitude-excitation frequency curves for different axial load at postbuckling state (\(P\geq P_{cr}\), \(m_{s}=0\), \(R=1k\Omega\), \(W_{0}=0.01h_{t}\), \(\kappa_{0}=0\) for distribution 1). Shown in Figure 10 are the dimensionless root mean square voltage (\(\frac{\kappa_{33}}{\kappa_{311}}\frac{V_{\rm rms}}{V_{\rm max}}\))-excitation frequency (\((\omega_{n}L^{2}/h_{t})\sqrt{12\rho_{\rm max}/C_{\rm max}}\)) curves for different axial loads at the postbuckling state (\(P\geq P_{cr}\), \(m_{s}=0\), \(R=1k\Omega\), \(W_{0}=0.01h_{t}\), \(\kappa_{0}=0\) for distribution 1). As the excitation frequency is close to the natural frequency of the structure, the root mean square voltage reaches a peak. As the axial load increases, the peak value increases, which is different from the postbuckling procedure shown in Figure 8. Further, the peak value of the root mean square voltage output for postbuckling procedure is remarkably larger than that for the prebuckling procedure. It provides a new idea to improve the mechanical electrical conversion efficiency of the structure. The mechanical electrical conversion efficiency in the postbuckling procedure is higher than that in the prebuckling procedure. Shown in Figure 11 are the dimensionless resonance amplitude (\(W_{\rm max}/W_{0}\))-axial load (\(\frac{12L^{2}P}{\kappa^{2}bC_{\rm max}h_{t}^{2}}\)) curves for different distributions of the core layer (\(m_{s}=0.5I_{0}L\), \(W_{0}=0.01h_{t}\), \(\kappa_{0}=0.5\), \(R=1k\Omega\)). The resonance amplitude is acquired when the excitation frequency matches the natural frequency of the structure. It seems that when the axial load is zero, the resonance amplitude shows no difference for three types of distribution. In the prebuckling procedure, as the axial load increases, the resonance amplitude decreases, and the difference between the three types of distribution increases. Distribution 2 has the largest resonance amplitude, and distribution 1 has the smallest resonance amplitude among these three types of distribution. In the postbuckling procedure, as the axial load increases, the resonance amplitude increases. Distribution 1 has the largest resonance amplitude, and distribution 2 has the smallest resonance amplitude among these three types of distribution. Figure 10: Dimensionless root mean square voltage output-excitation frequency curves for different axial load at postbuckling state (\(P\geq P_{cr}\), \(m_{s}=0\), \(R=1k\Omega\), \(W_{0}=0.01h_{t}\), \(\kappa_{0}=0\) for distribution 1). Shown in Figure 12 are the dimensionless optimal root mean square voltage output (\(\frac{4\kappa_{33}}{c_{311}}\frac{V_{max}}{W_{max}}\))-axial load (\(\frac{12L^{2}P}{\pi^{2}bC_{max}h_{t}^{2}}\)) curves for different distributions of the core layer (\(P\leq P_{cr}\), \(m_{s}=0.5I_{0}L\), \(W_{0}=0.01I_{t}\), \(\kappa_{0}=0.5\), \(R=1k\Omega\)). In the prebuckling procedure, it can be seen that the optimal RMS voltage decreases as the axial load increases, and there is little difference between the optimal RMS voltage of distribution 1 and distribution 3, and distribution 2 has the largest optimal RMS voltage. In the postbuckling procedure, as the axial load increases, the optimal RMS voltage increases. Distribution 1 has the largest optimal RMS voltage, and distribution 2 has the smallest optimal RMS voltage among these three type distributions.