Appendix
The elements of the matrix [\(a\)] in Eq. (53) are given by
$$\begin{aligned} a_{11}&= l_{z}, \quad a_{12} =\left( {1-\overline{{\delta }}_{\mathrm{p}_1 } } \right) \overline{{l}}_{z\mathrm{p}_1 }, \quad a_{13} =\left( {1-\overline{{\delta }}_{\mathrm{p}_2 } } \right) \overline{{l}}_{z\mathrm{p}_2 }, \quad a_{14} =\left( {1-\overline{{\delta }}_\mathrm{s} } \right) l_x , \\ a_{15}&= -\left( {1-\overline{{\delta }}_{\mathrm{p}_1 } } \right) \overline{{l}}_{z\mathrm{p}_1 } , \quad a_{16}= -\left( {1-\overline{{\delta }}_{\mathrm{p}_2 } } \right) \overline{{l}}_{z\mathrm{p}_2 }, \quad a_{17} =\left( {1-\overline{{\delta }}_\mathrm{s} } \right) \overline{{l}}_x , \quad a_{18}=0, \\ a_{19}&= 0, \quad a_{1,10}=0, \quad a_{1,11}=0; \quad a_{21}={\omega }^{2}{\rho }_\mathrm{w}, \\ a_{22}&= -\left( {H-\overline{{\delta }}_{\mathrm{p}_1 } C} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) +2\mu l_x^2 , \quad a_{23} =-\left( {H-\overline{{\delta }}_{\mathrm{p}_2 } C} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) +2\mu l_x^2 ,\\ a_{24}&= -2Gl_x \overline{{l}}_{z\mathrm{s}}, \quad a_{25} =-\left( {H-\overline{{\delta }}_{\mathrm{p}_1 } C} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) +2\mu l_x^2 , \\ a_{26}&= -\left( {H-\overline{{\delta }}_{\mathrm{p}_2 } C} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) +2\overline{{G}}l_x^2 ,\quad a_{27} = 2\mu l_x \overline{{l}}_{z\mathrm{s}},\\ a_{28}&= 0, \quad a_{29}=0, \quad a_{2,10} =0, \quad a_{2,11} =0; \quad a_{31} = {\omega }^{2}{\rho }_\mathrm{w},\\ a_{32}&= \left( {-C+\overline{{\delta }}_{\mathrm{p}_1 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) , \quad a_{33} =\left( {-C+\overline{{\delta }}_{\mathrm{p}_2 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) ,\\ a_{34}&= 0,\quad a_{35} =\left( {-C+\overline{{\delta }}_{\mathrm{p}_1 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) , \quad a_{36} =\left( {-C+\overline{{\delta }}_{\mathrm{p}_2 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) , \\ a_{37}&= 0,\quad a_{38} =0, \quad a_{39} = 0, \quad a_{3,10} = 0, \quad a_{3,11} = 0;\quad a_{41}=0, \\ a_{42}&= 2l_x \overline{{l}}_{z\mathrm{p}_1 }, \quad a_{43} =2l_x \overline{{l}}_{z\mathrm{p}_2 }, \quad a_{44} =-\overline{{l}}_{z\mathrm{s}}^2 +l_x^2, a_{45} =-2l_x \overline{{l}}_{z\mathrm{p}_1 }, \quad a_{46} =-2l_x\overline{{l}}_{z\mathrm{p}_2 },\\ a_{47}&= -\overline{{l}}_{z\mathrm{s}}^2 +l_x^2 , a_{48}=0, \quad a_{49} = 0, \quad a_{4,10} = 0, \quad a_{4,11}=0;\quad a_{51}=0, \\ a_{52}&= -\overline{{l}}_{z\mathrm{p}_1 } \exp \left( {-i\overline{{l}}_{z\mathrm{p}_1 } h} \right) , \quad a_{53} =-\overline{{l}}_{z\mathrm{p}_2 } \exp \left( {-i\overline{{l}}_{z\mathrm{p}_2 }h} \right) , \quad a_{54} =-l_x \exp \left( {-i\overline{{l}}_{z\mathrm{s}} h} \right) ,\\ a_{55}&= \overline{{l}}_{z\mathrm{p}_1 } \exp \left( {i\overline{{l}}_{z\mathrm{p}_1} h} \right) , \quad a_{56} =\overline{{l}}_{z\mathrm{p}_2 } \exp \left( {i\overline{{l}}_{z\mathrm{p}_2 } h} \right) , \quad a_{57} =-l_x \exp \left( {i\overline{{l}}_{z\mathrm{s}} h} \right) , \end{aligned}$$
$$\begin{aligned} a_{58}&= l_{z\mathrm{p}_1 } \exp \left( {-il_{z\mathrm{p}_1 } h} \right) ,\quad a_{59}= l_{z\mathrm{p}_2 } \exp \left( {-il_{z\mathrm{p}_2 } h} \right) , \quad a_{5,10} =l_{z\mathrm{p}_3 } \exp \left( {-il_{z\mathrm{p}_3 } h} \right) , \\ a_{5,11}&= l_{x} \exp (-{il}_{z\mathrm{s}}h);\quad a_{61}=0, \quad a_{62} =-l_x \exp \left( {-i\overline{{l}}_{z\mathrm{p}_1 } h} \right) , \quad a_{63} =-l_x \exp \left( {-i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\\ a_{64}&= \overline{{l}}_{z\mathrm{s}} \exp \left( {-i\overline{{l}}_{z\mathrm{s}} h} \right) ,\quad a_{65} =-l_x \exp \left( {i\overline{{l}}_{z\mathrm{p}_1 } h} \right) ,\quad a_{66} =-l_x \exp \left( {i\overline{{l}}_{z\mathrm{p}_2 } h} \right) , \\ a_{67}&= -\overline{{l}}_{z\mathrm{s}} \exp \left( {i\overline{{l}}_{z\mathrm{s}} h} \right) ,\quad a_{68} =l_x \exp \left( {-il_{z\mathrm{p}_1 } h} \right) ,\quad a_{69} =l_x \exp \left( {-il_{z\mathrm{p}_2 } h} \right) , \\ a_{6,10}&= l_x \exp \left( {-il_{z\mathrm{p}_3 } h} \right) ,\quad a_{6,11}=-l_{z\mathrm{s}} \exp (- il_{z\mathrm{s}}h); \quad a_{71} = 0,\\ a_{72}&= \left[ {-\left( {H-\overline{{\delta }}_{\mathrm{p}_{1} } C} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) +2\overline{{G}}l_x^2 } \right] \exp \left( {-i\overline{{l}}_{z\mathrm{p}_1 } h} \right) ,\\ a_{73}&= \left[ {-\left( {H-\overline{{\delta }}_{\mathrm{p}_{2} } C} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) +2\overline{{G}}l_x^2 } \right] \exp \left( {-i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\\ a_{74}&= -2\overline{{G}}l_x \overline{{l}}_{z\mathrm{s}} \exp (-i\overline{{l}}_{z\mathrm{s}} h),\\ a_{75}&= \left[ {-\left( {H-\overline{{\delta }}_{\mathrm{p}_{1} } C} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) +2\overline{{G}}l_x^2 } \right] \exp \left( {i\overline{{l}}_{z\mathrm{p}_1 } h} \right) ,\\ a_{76}&= \left[ {-\left( {H-\overline{{\delta }}_{\mathrm{p}_{2}}C}\right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) +2\overline{{G}}l_x^2 } \right] \exp \left( {i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\\ a_{77}&= 2\overline{{G}}l_x \overline{{l}}_{z\mathrm{s}} \exp (i\overline{{l}}_{z\mathrm{s}} h),\\ a_{78}&= \left\{ (K_\mathrm{u} -\frac{2}{3}G)(l_{z\mathrm{p}_1 }^2 +l_x^2 )+2Gl_{z\mathrm{p}_1 }^2\right. \\&\left. -K_\mathrm{u} \left[ {B^{(1)}v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_1 } ^{(1)})+B^{(2)}v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_1 } ^{(2)})} \right] (l_{z\mathrm{p}_1 }^2 +l_x^2 ) \right\} \exp \left( {-i\overline{{l}}_{z\mathrm{p}_1 } h}\right) ,\\ a_{79}&= \left\{ (K_\mathrm{u} -\frac{2}{3}G)(l_{z\mathrm{p}_2 }^2 +l_x^2 )+2Gl_{z\mathrm{p}_2 }^2\right. \\&\left. -K_\mathrm{u} \left[ {B^{(1)}v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_2 } ^{(1)})+B^{(2)}v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_2 } ^{(2)})} \right] (l_{z\mathrm{p}_2 }^2 +l_x^2 ) \right\} \exp \left( {-i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\\ a_{7,10}&= \left\{ (K_\mathrm{u} -\frac{2}{3}G)(l_{z\mathrm{p}_3 }^2 +l_x^2 )+2Gl_{z\mathrm{p}_3 }^2\right. \\&\left. -K_\mathrm{u} \left[ {B^{(1)}v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_3 } ^{(1)})+B^{(2)}v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_3 } ^{(2)})} \right] (l_{z\mathrm{p}_3 }^2 +l_x^2 ) \right\} \exp \left( {-i\overline{{l}}_{z\mathrm{p}_3 } h} \right) , \end{aligned}$$
$$\begin{aligned} a_{7,11}&= 2{Gl}_{x}l_{z\mathrm{s}}\,\exp (-{il}_{z\mathrm{s}}h); \quad a_{81} = 0, \quad a_{82} =2\overline{{G}}l_x \overline{{l}}_{z\mathrm{p}_1 } \exp \left( {-i\overline{{l}}_{z\mathrm{p}_1 } h} \right) , \\ a_{83}&= 2\overline{{G}}l_x \overline{{l}}_{z\mathrm{p}_2 } \exp \left( {-i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\quad a_{84} =\overline{{G}}\left( {-\overline{{l}}_{z\mathrm{s}}^2 +l_x^2 } \right) \exp \left( {-i\overline{{l}}_{z\mathrm{s}} h} \right) , \\ a_{85}&= -2\overline{{G}}l_x \overline{{l}}_{z\mathrm{p}_1 } \exp \left( {i\overline{{l}}_{z\mathrm{p}_1 } h} \right) ,\quad a_{86} = -2\overline{{G}}l_x \overline{{l}}_{z\mathrm{p}_2 } \exp \left( {i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\\ a_{87}&= \overline{{G}}\left( {-\overline{{l}}_{z\mathrm{s}}^2 +l_x^2 } \right) \exp \left( {i\overline{{l}}_{z\mathrm{s}} h} \right) , \quad a_{88} =-2Gl_x l_{z\mathrm{p}_1 } \exp \left( {-il_{z\mathrm{p}_1 } h} \right) , \\ a_{89}&= -2Gl_x l_{z\mathrm{p}_2 } \exp \left( {-il_{z\mathrm{p}_2 } h} \right) ,\\ a_{8,10}&= -2Gl_x l_{z\mathrm{p}_3 } \exp \left( {-il_{z\mathrm{p}_3 } h} \right) , \quad a_{8,11}= G(l_{z\mathrm{s}}^{2}-l_{x}^{2})\exp (-{il}_{z\mathrm{s}}h);\\ a_{91}&= 0, \quad a_{92} =\left( {C-\overline{{\delta }}_{\mathrm{p}_1 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) \exp \left( {-i\overline{{l}}_{z\mathrm{p}_1 } h} \right) ,\\ a_{93}&= \left( {C-\overline{{\delta }}_{\mathrm{p}_2 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) \exp \left( {-i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\\ a_{94}&= 0,\quad a_{95} =\left( {C-\overline{{\delta }}_{\mathrm{p}_1 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) \exp \left( {i\overline{{l}}_{z\mathrm{p}_1 } h} \right) , \\ a_{96}&= \left( {C-\overline{{\delta }}_{\mathrm{p}_2 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) \exp \left( {i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\quad a_{97}=0,\\ a_{98}&= \left[ {-A_{13} +A_{23} v^{(1)} \varphi ^{(1)}(1-\delta _{\mathrm{p}_1 } ^{(1)})+A_{33} v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_1 } ^{(2)})} \right] (l_x ^{2}+l_{z\mathrm{p}_1 } ^{2})\exp (-il_{z\mathrm{p}_1 } h),\\ a_{99}&= \left[ {-A_{13} +A_{23} v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_2 } ^{(1)})+A_{33} v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_2 } ^{(2)})} \right] (l_x ^{2}+l_{z\mathrm{p}_2 } ^{2})\exp (-il_{z\mathrm{p}_2 } h),\\ a_{9,10}&= \left[ {-A_{13} +A_{23} v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_3 } ^{(1)})+A_{33} v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_3 } ^{(2)})} \right] (l_x ^{2}+l_{z\mathrm{p}_3 } ^{2})\exp (-il_{z\mathrm{p}_3 } h),\\ a_{9,11}&= 0\ \hbox {(if the open-pore boundary condition is applied) or} \end{aligned}$$
$$\begin{aligned} a^{\prime }_{91}&= a^{\prime }_{92}=a^{\prime }_{93}=a^{\prime }_{94}=a^{\prime }_{95}=a^{\prime }_{96}=a^{\prime }_{97}=0, \quad {a}'_{98} =l_{z\mathrm{p}_1 } (1-\delta _{\mathrm{p}_1 } ^{(2)})\exp (-il_{z\mathrm{p}_1 } h),\\ {a}'_{99}&= l_{z\mathrm{p}_2 } (1-\delta _{\mathrm{p}_2 } ^{(2)})\exp (-il_{z\mathrm{p}_2 } h),\quad {a}'_{9,10} =l_{z\mathrm{p}_3 } (1-\delta _{\mathrm{p}_3 } ^{(2)})\exp (-il_{z\mathrm{p}_3 } h), \\ {a}'_{9,11}&= l_x (1-\delta _\mathrm{s} ^{(2)})\exp (-il_{z\mathrm{p}_1 } h)\exp (-il_{z\mathrm{s}} h)\\&\quad \hbox {(if the sealed-pore boundary condition is applied)}; \\ a_{10,1}&= 0,\quad a_{10,2} = \left( {C-\overline{{\delta }}_{\mathrm{p}_1 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) \exp \left( {-i\overline{{l}}_{z\mathrm{p}_1 } h} \right) ,\\ a_{10,3}&= \left( {C-\overline{{\delta }}_{\mathrm{p}_2 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) \exp \left( {-i\overline{{l}}_{z\mathrm{p}_2 } h} \right) , \quad a_{10,4}=0,\\ a_{10,5}&= \left( {C-\overline{{\delta }}_{\mathrm{p}_1 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_1 }^2 +l_x^2 } \right) \exp \left( {i\overline{{l}}_{z\mathrm{p}_1 } h} \right) ,\\ a_{10,6}&= \left( {C-\overline{{\delta }}_{\mathrm{p}_2 } M} \right) \left( {\overline{{l}}_{z\mathrm{p}_2 }^2 +l_x^2 } \right) \exp \left( {i\overline{{l}}_{z\mathrm{p}_2 } h} \right) ,\quad a_{10,7}=0,\\ a_{10,8}&= \left[ {-A_{12} +A_{22} v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_1 } ^{(1)})+A_{23} v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_1 } ^{(2)})} \right] (l_x ^{2}+l_{z\mathrm{p}_1 } ^{2})\exp (-il_{z\mathrm{p}_1 } h),\\ a_{10,9}&= \left[ {-A_{12} +A_{22} v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_2 } ^{(1)})+A_{23} v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_2 } ^{(2)})} \right] (l_x ^{2}+l_{z\mathrm{p}_2 } ^{2})\exp (-il_{z\mathrm{p}_2 } h),\\ a_{10,10}&= \left[ {-A_{12} +A_{22} v^{(1)}\varphi ^{(1)}(1-\delta _{\mathrm{p}_3 } ^{(1)})+A_{23} v^{(2)}\varphi ^{(2)}(1-\delta _{\mathrm{p}_3 } ^{(2)})} \right] (l_x ^{2}+l_{z\mathrm{p}_3 } ^{2})\exp (-il_{z\mathrm{p}_3 } h),\\ a_{10,11}&= 0\ \hbox {(if the open-pore boundary condition is applied) or} \end{aligned}$$
$$\begin{aligned} a^{\prime }_{10,1}&= a^{\prime }_{10,2}=a^{\prime }_{10,3}=a^{\prime }_{10,4}=a^{\prime }_{10,5}=a^{\prime }_{10,6}=a^{\prime }_{10,7}=0,\\ {a}'_{10,8}&= l_{z\mathrm{p}_1 } (1-\delta _{\mathrm{p}_1 } ^{(1)})\exp (-il_{z\mathrm{p}_1 } h),{a}'_{10,9} =l_{z\mathrm{p}_2 } (1-\delta _{\mathrm{p}_2 } ^{(1)})\exp (-il_{z\mathrm{p}_2 } h),\\ {a}'_{10,10}&= l_{z\mathrm{p}_3 } (1-\delta _{\mathrm{p}_3 } ^{(1)})\exp (-il_{z\mathrm{p}_3 } h),\\ a^{\prime }_{10,11}&= l_{x}(1-{\delta }_\mathrm{s}^{(1)})\exp (-{il}_{z\mathrm{s}}h)\ \hbox {(if the sealed-pore boundary condition is applied)};\\ a_{11,1}&= 0,\\ a_{11,2}&= -\overline{{l}}_{z\mathrm{p}_1 } \overline{{\delta }}_{\mathrm{p}_1 } \exp (-i\overline{{l}}_{z\mathrm{p}_1 } h),\\ a_{11,3}&= -\overline{{l}}_{z\mathrm{p}_2 } \overline{{\delta }}_{\mathrm{p}_2 } \exp (-i\overline{{l}}_{z\mathrm{p}_2 } h),\\ a_{11,4}&= -\overline{{l}}_x \overline{{\delta }}_\mathrm{s} \exp (-i\overline{{l}}_{z\mathrm{s}} h),\\ a_{11,5}&= \overline{{l}}_{z\mathrm{p}_1 } \overline{{\delta }}_{\mathrm{p}_1 } \exp (i\overline{{l}}_{z\mathrm{p}_1 } h),\\ a_{11,6}&= \overline{{l}}_{z\mathrm{p}_2 } \overline{{\delta }}_{\mathrm{p}_2 } \exp (i\overline{{l}}_{z\mathrm{p}_2 } h),\\ a_{11,7}&= -l_x \overline{{\delta }}_\mathrm{s} \exp (i\overline{{l}}_{z\mathrm{s}} h),\\ a_{11,8}&= \left[ {v^{(1)}\varphi ^{(1)}(\overline{{\delta }}_{\mathrm{p}_1 } ^{(1)}-1)+v^{(2)}\varphi ^{(2)}(\overline{{\delta }}_{\mathrm{p}_1 } ^{(2)}-1)} \right] l_{z\mathrm{p}_1 } \exp (-il_{z\mathrm{p}_1 } h),\\ a_{11,9}&= \left[ {v^{(1)}\varphi ^{(1)}(\overline{{\delta }}_{\mathrm{p}_2 } ^{(1)}-1)+v^{(2)}\varphi ^{(2)}(\overline{{\delta }}_{\mathrm{p}_2 } ^{(2)}-1)} \right] l_{z\mathrm{p}_2 } \exp (-il_{z\mathrm{p}_2 } h),\\ a_{11,10}&= \left[ {v^{(1)}\varphi ^{(1)}(\overline{{\delta }}_{\mathrm{p}_3 } ^{(1)}-1)+v^{(2)}\varphi ^{(2)}(\overline{{\delta }}_{\mathrm{p}_3 } ^{(2)}-1)} \right] l_{z\mathrm{p}_3 } \exp (-il_{z\mathrm{p}_3 } h),\\ a_{11,11}&= \left[ {v^{(1)}\varphi ^{(1)}(\delta _\mathrm{s} ^{(1)}-1)+v^{(2)}\varphi ^{(2)}(\delta _\mathrm{s} ^{(2)}-1)} \right] l_{z\mathrm{s}} \exp (-il_{z\mathrm{s}} h)\\&\quad {\hbox {(if the open-pore boundary condition is applied) or}}\\ a^{\prime }_{11,1}&= 0,{a}'_{11,2} =-\overline{{l}}_{z\mathrm{p}_1 } \overline{{\delta }}_{\mathrm{p}_1 } \exp (-i\overline{{l}}_{z\mathrm{p}_1 } h),{a}'_{11,3} =-\overline{{l}}_{z\mathrm{p}_2 } \overline{{\delta }}_{\mathrm{p}_2 } \exp (-i\overline{{l}}_{z\mathrm{p}_2 } h),\\ {a}'_{11,4}&= -l_x \overline{{\delta }}_\mathrm{s} \exp (-i\overline{{l}}_{z\mathrm{s}} h),\\ {a}'_{11,5}&= \overline{{l}}_{z\mathrm{p}_1 } \overline{{\delta }}_{\mathrm{p}_1 } \exp (i\overline{{l}}_{z\mathrm{p}_1 } h),{a}'_{11,6} =\overline{{l}}_{z\mathrm{p}_2 } \overline{{\delta }}_{\mathrm{p}_2 } \exp (i\overline{{l}}_{z\mathrm{p}_2 } h), {a}'_{11,7} =-l_x \overline{{\delta }}_\mathrm{s} \exp (i\overline{{l}}_{z\mathrm{s}} h),\\ a^{\prime }_{11,8}&= 0, \quad a^{\prime }_{11,9}=0, \quad a^{\prime }_{11,10}=0, \quad a^{\prime }_{11,11}=0\\&\quad \hbox {(if the sealed-pore boundary condition is applied)}. \end{aligned}$$
The elements of the matrix [b] in Eq. (53) are given by
$$\begin{aligned}&b_{1}=l_{z}, \quad b_{2}=-{\omega }^{2}{ \rho }_{w}, \quad b_{3}=-{\omega }^{2}{\rho }_{w},\\&\quad b_{4}=b_{5}=b_{6}=b_{7}=b_{8}=b_{9}=b_{10}=b_{11}=0. \end{aligned}$$
