this hypothesis, the scaled vDOS $g(\omega)/(\omega^2 A_\mathrm{D})$ is plotted as a function of the scaled frequency $\omega/\omega_\mathrm{D}$ and presented in Fig. \[fig6\]. As discussed above, $A_\mathrm{D}$ and $\omega_\mathrm{D}$ are determined mostly by the shear modulus $G$. Although deviations are observed for $L=50$, the scaled vDOSs collapse for different values of $\varepsilon_\mathrm{bend}$. In particular, an exact collapse is obtained for $L=3$. This result indicates that the effects engendered by the bending rigidity on the low-frequency spectra are comprised of the the shear modulus changes. A same collapse was observed in effects of pressure on the BP in the covalent-bonding network glass (Na$_2$FeSi$_3$O$_8$) [@Monaco_2006]. In addition, a previous experiment [@Caponi_2011] demonstrated that the effects of the polymerization are also comprised by the macroscopic elasticity changes. The collapsed results for (a) $L=50$ and (b) $L=3$ are consistent with the experimental observation.

According to the collapses observed in Fig. \[fig6\], $\omega_\mathrm{BP} / \omega_\mathrm{D}$ does not depend on $\varepsilon_\mathrm{bend}$. As stated previously, when $\varepsilon_\mathrm{bend}$ varies, $\omega_\mathrm{D}
\propto \rho^{1/3} c_\mathrm{T} \propto \rho^{-1/6} \sqrt{G}$. As $\rho$ varies in a range of 15%, as shown in Fig. \[fig1\], the effect of $\rho$ on $\omega_\mathrm{D}$ is weak. Thus, $\omega_\mathrm{D}$ is approximately proportional to $\sqrt{G}$, which leads to $\omega_\mathrm{BP} \propto 