AI 中文总结
本文比较了线性粘弹性中Becker、Lomnitz和Lambert模型的比耗散，推导了其渐近公式及广义Becker和扩展Jeffreys--Lomnitz模型的新闭式表达式，并恢复了Maxwell模型极限。
AI 中文摘要
我们比较了线性粘弹性中Becker、Lomnitz和Lambert模型的比耗散$Q^{-1}\left( \omega \right) $。从图形上看，当$\omega \rightarrow 0^{+}$和$\omega \rightarrow +\infty$时，这些模型的比耗散行为相似。此外，我们获得了Becker和Lomnitz模型在$\omega \rightarrow 0^{+}$和$\omega \rightarrow +\infty$时$Q^{-1}\left( \omega \right) $渐近行为的解析公式，其中后一极限与Maxwell模型的比耗散一致。我们还推导了广义Becker模型中当参数$\nu \in \left( 0,1\right] $为有理数时比耗散$Q_{\nu }^{-1}\left( \omega \right) $的一个新的闭式表达式。当$\nu \rightarrow 0$时，我们恢复Maxwell模型的比耗散，而当$\nu =1$时，我们恢复原始Becker模型的比耗散。此外，我们推导了扩展Jeffreys--Lomnitz模型$Q_{\alpha }^{-1}\left( \omega \right) $的两个新的闭式表达式，第一个适用于$\alpha \in \left( 0,1\right] $，第二个适用于$\alpha \in \left( -\infty,1\right] $。当$\alpha \rightarrow 0$时，我们恢复Lomnitz模型的比耗散，而当$\alpha =1$时，我们恢复Maxwell模型的比耗散。最后，我们得出结论：当$\omega \rightarrow +\infty$时，$Q_{\alpha }^{-1}\left( \omega \right) $的渐近行为与Maxwell模型的比耗散一致。
英文摘要
We compare the specific dissipation $Q^{-1}\left( ω\right) $ for the Becker, Lomnitz, and Lambert models in linear viscoelasticity. Graphically, the specific dissipation of these models behaves similarly as $ω\rightarrow 0^{+}$ and $ω\rightarrow +\infty$. Furthermore, we obtain analytic formulas for the asymptotic behavior of $Q^{-1}\left( ω\right) $ in the Becker and Lomnitz models as $ω\rightarrow 0^{+}$ and $ω\rightarrow +\infty$, where the latter limit coincides with the specific dissipation of the Maxwell model. We also derive a novel closed-form expression for the specific dissipation in the generalized Becker model, $Q_{ν}^{-1}\left( ω\right) $, when the parameter $ν\in \left( 0,1\right] $ is rational. When $ν\rightarrow 0$, we recover the specific dissipation of the Maxwell model, whereas when $ν=1$, we recover that of the original Becker model. In addition, we derive two new closed-form expressions for the specific dissipation for the extended Jeffreys--Lomnitz model $Q_{α}^{-1}\left( ω\right) $, the first being valid for $α\in \left( 0,1\right] $, and the second for $α\in \left( -\infty ,1\right] $. When $α\rightarrow 0$, we recover the specific dissipation of the Lomnitz model, whereas when $α=1$, we recover that of the Maxwell model. Finally, we conclude that the asymptotic behavior of $Q_{α}^{-1}\left( ω\right) $ as $ω\rightarrow +\infty $ coincides with the specific dissipation of the Maxwell model. Keywords:
Comments27 pages, 3 figures
Journal refMathematics, Vol. 14, No 16 (2026), 2936
