Table 2.

Governing equations, boundary conditions and constitutive relations

Airflow domain (a) $\{\begin{array}{l}{\oint }_{\partial (V^f)}(\mathbf{v}-{\mathbf{v}}_g)·\mathrm{d}\mathbf{S}=0\hfill \\ {\rho }_f\frac{\mathrm{d}}{\mathrm{d}t}{\int }_{V^f}\mathbf{v}\mathrm{d}V+{\rho }_f{\oint }_{\partial (V^f)}\mathbf{v}(\mathbf{v}-{\mathbf{v}}_g)·\mathrm{d}\mathbf{S}=-{\oint }_{\partial (V^f)}p\mathbf{I}·\mathrm{d}\mathbf{S}+{\oint }_{\partial (V^f)}{\mathit{\tau }}_f·\mathrm{d}\mathbf{S}\hfill \end{array}$ (b)τf= μ[▽v + (▽v)T] (c) $\{\begin{array}{l}p(x_{\text{is}}=-T_{\text{entry}}-T)=p_{\text{in}}(t)\hfill \\ p(x_{\text{is}}=T_{\text{exit}})=0,\hfill \\ \mathbf{v}(x_{\text{ap}}=\pm L/2)={\mathbf{v}}_g(x_{\text{ap}}=\pm L/2)=0,\hfill \\ \mathbf{v}(x_{\text{ml}}=\pm W/2)={\mathbf{v}}_{\mathrm{g}}(x_{\text{ml}}=\pm W/2)=0\hfill \end{array}$

Vocal fold domain (d) ${\int }_{V^s}\mathit{\sigma }:\delta {\mathit{D}}_v\mathrm{d}V-{\oint }_{\partial (V^s)}{\mathit{\tau }}_s·\delta {\mathbf{u}}_v\mathrm{d}S-{\int }_{V^s}{\rho }_s\ddot{\mathbf{u}}·\delta {\mathbf{u}}_v\mathrm{d}V$ (e) $\{\begin{array}{l}\mathit{\sigma }(t)={\int }_0^{t}2G(t-t^{\prime })\stackrel{.}{\mathit{e}}\mathrm{d}{t}^{\prime }+\mathit{I}{\int }_0^{t}K(t-t^{\prime })\stackrel{.}{\epsilon }\mathrm{d}{t}^{\prime }\hfill \\ G(t)=\frac{E}{2(1+\nu )}\left[1-g_1+g_1{\mathrm{e}}^{-t/{\tau }_1}\right]\hfill \\ K(t)=\frac{E}{3(1-2\nu )}\left[1-k_1+k_1{\mathrm{e}}^{-t/{\tau }_1}\right]\hfill \end{array}$ (f)u(xap= ± L/2) = 0, u(xml = ±W/2) = 0