Appendix A
$$ \begin{aligned} N_{1} = & - ((\sinh [(\eta + h_{1} )\alpha_{2} ]G_{y} {\kern 1pt} \Delta_{1} (g^{2} s^{2} - M_{2}^{2} ) \\ & + {\text{e}}^{{2\lambda h_{1} }} \sinh [h_{3} \alpha_{1} ]\tilde{c}_{44} k_{13} \alpha_{1} \,\Delta_{2} )( - \cosh [h_{2} \alpha_{1} ]G_{y} k_{12} \,\Delta_{3} + \sinh [h_{2} \alpha_{1} ]{\kern 1pt} \,\tilde{c}_{44} \alpha_{1} \,\Delta_{4} )) \\ \end{aligned} $$
$$ \begin{aligned} N_{2} = & (\alpha_{2} ( - {\text{e}}^{{2\lambda h_{1} }} \sinh [h_{1} \alpha_{2} ]\sinh [h_{2} \alpha_{1} ]\sinh [h_{3} \alpha_{1} ]\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} + \sinh [h_{1} \alpha_{2} ]G_{y}^{2} \,\Delta_{5} ( - \Delta_{1} )(g^{2} s^{2} - M_{2}^{2} ) \\ & + \tilde{c}_{44} G_{y} \alpha_{1} ( - {\text{e}}^{{2\lambda h_{1} }} \cosh [h_{2} \alpha_{1} ]\sinh [h_{3} \alpha_{1} ]k_{12} k_{13} \,\Delta_{6} \\ + \sinh [h_{2} \alpha_{1} ]({\text{e}}^{{2\lambda h_{1} }} \sinh [h_{3} \alpha_{1} ]\tilde{c}_{44} k_{13} \alpha_{1} \,\Delta_{6} - k_{12} \,\Delta_{1} \,\Delta_{7} )))) \\ \end{aligned} $$
$$ \begin{aligned} N_{3} = & - ((\sinh [(\eta + h_{1} )\alpha_{2} ]G_{y} \,\Delta_{1} (g^{2} s^{2} - M_{2}^{2} ) \\ & + {\text{e}}^{{2\lambda h_{1} }} \sinh [h_{3} \alpha_{1} ]\tilde{c}_{44} k_{13} \alpha_{1} \Delta_{2} )( - \cosh [h_{2} \alpha_{1} ]G_{y} k_{12} \sinh [\alpha_{2} y](g^{2} s^{2} - M_{2}^{2} ) + \sinh [h_{2} \alpha_{1} ]\tilde{c}_{44} \alpha_{1} \Delta_{8} )) \\ \end{aligned} $$
$$ N_{4} = ((\sinh [\eta \alpha_{2} ]G_{y} \Delta_{5} (g^{2} s^{2} - M_{2}^{2} ) - \sinh [h_{2} \alpha_{1} ]\,\tilde{c}_{44} k_{12} \alpha_{1} \,\Delta_{9} )(\cosh [h_{3} \alpha_{1} ]G_{y} k_{13} \Delta_{10} - \sinh [h_{3} \alpha_{1} ]\;\tilde{c}_{44} \alpha_{1} \Delta_{11} )) $$
$$ \begin{aligned} N_{5} = & ((\sinh [\eta \alpha_{2} ]G_{y} \Delta_{5} (g^{2} s^{2} - M_{2}^{2} ) \\ & - \sinh [h_{2} \alpha_{1} ]\tilde{c}_{44} k_{12} \alpha_{1} \Delta_{9} )(\cosh [h_{3} \alpha_{1} ]G_{y} k_{13} \sinh [\alpha_{2} (y + h_{1} )](g^{2} s^{2} - M_{2}^{2} ) - \sinh [h_{3} \alpha_{1} ]\;\tilde{c}_{44} \alpha_{1} \Delta_{12} )) \\ \end{aligned} $$
$$ \Delta_{1} = (\cosh [h_{3} \alpha_{1} ]k_{13} - \sinh [h_{3} \alpha_{1} ]\tilde{c}_{44} \alpha_{1} )$$
$$\Delta_{2} = (\alpha_{2} \cosh [(\eta + h_{1} )\alpha_{2} ] - \lambda \sinh [(\eta + h_{1} )\alpha_{2} ]) $$
$$ \Delta_{3} = (\lambda \sinh [\alpha_{2} y] + \alpha_{2} \cosh [\alpha_{2} y])$$
$$\Delta_{4} = ((k_{12} + G_{y} \lambda )\sinh [\alpha_{2} y] + G_{y} \alpha_{2} \cosh [\alpha_{2} y])) $$
$$ \Delta_{5} = (\cosh [h_{2} \alpha_{1} ]k_{12} - \sinh [h_{2} \alpha_{1} ]\tilde{c}_{44} \alpha_{1} )$$
$$\Delta_{6} = (\alpha_{2} \cosh [\alpha_{2} h_{1} ] - \lambda \sinh [\alpha_{2} h_{1} ]) $$
$$ \Delta_{7} = (\alpha_{2} \cosh [\alpha_{2} h_{1} ] + \lambda \sinh [\alpha_{2} h_{1} ]) $$
$$ \Delta_{8} = (( - \lambda {\kern 1pt} k_{12} + G_{y} (g^{2} s^{2} - M_{2}^{2} ))\sinh [\alpha_{2} y] + k_{12} \alpha_{2} \cosh [\alpha_{2} y]) $$
$$ \Delta_{9} = (\alpha_{2} \cosh [\eta \alpha_{2} ] - \lambda \sinh [\eta \alpha_{2} ]) $$
$$ \Delta_{10} = (\lambda \sinh [\alpha_{2} (y + h_{1} )] + \alpha_{2} \cosh [\alpha_{2} (y + h_{1} )]) $$
$$ \Delta_{11} = (( - {\text{e}}^{{2\lambda h_{1} }} k_{13} + G_{y} \lambda )\sinh [\alpha_{2} (y + h_{1} )] + G_{y} \alpha_{2} \cosh [\alpha_{2} (y + h_{1} )]) $$
$$ \Delta_{12} = (({\text{e}}^{{2\lambda h_{1} }} \lambda {\kern 1pt} k_{13} + G_{y} (g^{2} s^{2} - M_{2}^{2} ))\sinh [\alpha_{2} (y + h_{1} )] - {\text{e}}^{{2\lambda h_{1} }} \alpha_{2} k_{13} \cosh [\alpha_{2} (y + h_{1} )]) $$
$$ \alpha_{1} = \sqrt {s^{2} - M_{1}^{2} } $$
$$ \alpha_{2} = \sqrt {\lambda^{2} + g^{2} s^{2} - M_{2}^{2} } $$
Appendix B
$$ \begin{aligned} C_{1} = & \tanh [\alpha_{1} (\eta - h_{2} )]\{ \,\varOmega_{8} \cosh (\alpha_{1} \eta ){\kern 1pt} {\kern 1pt} + G_{y}^{2} \,\varOmega_{5} \varOmega_{1} \sinh (\alpha_{2} h_{1} )(g^{2} s^{2} - M_{2}^{2} ) \\ + \tilde{c}_{44} G_{y} \alpha_{1} [{\text{e}}^{{2\lambda h_{1} }} k_{13} \,\varOmega_{5} \varOmega_{3} \sinh (\alpha_{1} h_{3} ) + k_{12} \,\varOmega_{1} \,\varOmega_{4} \cosh (\alpha_{1} \eta )]\} \\ \end{aligned} $$
$$ \begin{aligned} C_{2} = & \tilde{c}_{44} G_{y} \alpha_{1} [{\text{e}}^{{2\lambda h_{1} }} k_{13} \varOmega_{2} \,\varOmega_{3} \sinh (\alpha_{1} h_{3} ) + k_{12} \,\varOmega_{1} \,\varOmega_{4} \sinh (\alpha_{1} h_{2} )] + \varOmega_{8} \sinh (\alpha_{1} h_{2} )\, \\ & \quad + \sinh (\alpha_{2} h_{1} )G_{y}^{2} \,\varOmega_{2} \,\varOmega_{1} (g^{2} s^{2} - M_{2}^{2} ) \\ \end{aligned} $$
$$ \begin{aligned} C_{3} = & \sinh [\alpha_{1} (\eta - h_{2} )]\{ \varOmega_{8} \cosh (\alpha_{1} y) + G_{y}^{2} {\kern 1pt} \varOmega_{6} {\kern 1pt} \varOmega_{1} \sinh (\alpha_{2} h_{1} )(g^{2} s^{2} - M_{2}^{2} ) \\ \quad + \tilde{c}_{44} G_{y} \alpha_{1} [{\text{e}}^{{2\lambda h_{1} }} k_{13} \varOmega_{6} {\kern 1pt} \varOmega_{3} \sinh (\alpha_{1} h_{3} ) + k_{12} \varOmega_{1} {\kern 1pt} \varOmega_{4} \cosh (\alpha_{1} y)]\} \\ \end{aligned} $$
$$ \begin{aligned} C_{4} = & \alpha_{1} \sinh [\alpha_{1} (\eta - h_{2} )]\{ \varOmega_{8} \sinh (\alpha_{1} y)\, + G_{y}^{2} {\kern 1pt} \varOmega_{7} {\kern 1pt} \varOmega_{1} \sinh (\alpha_{2} h_{1} )(g^{2} s^{2} - M_{2}^{2} ) \\ + \tilde{c}_{44} G_{y} \alpha_{1} [{\text{e}}^{{2\lambda h_{1} }} k_{13} \varOmega_{7} \varOmega_{3} \sinh (\alpha_{1} h_{3} ) + k_{12} \varOmega_{1} \varOmega_{4} \sinh (\alpha_{1} y)]\} \\ \end{aligned} $$
$$ \varOmega_{1} = \tilde{c}_{44} \alpha_{1} \sinh (\alpha_{1} h_{3} ) - k_{13} \cosh (\alpha_{1} h_{3} ),$$
$$\varOmega_{2} = k_{12} \cosh (\alpha_{1} h_{2} ) - \tilde{c}_{44} \alpha_{1} \sinh (\alpha_{1} h_{2} ) $$
$$ \varOmega_{3} = \lambda \sinh (\alpha_{2} h_{1} ) - \alpha_{2} \cosh (\alpha_{2} h_{1} ),$$
$$\varOmega_{4} = \lambda \sinh (\alpha_{2} h_{1} ) + \alpha_{2} \cosh (\alpha_{2} h_{1} ) $$
$$ \varOmega_{5} = k_{12} \sinh (\alpha_{1} \eta ) - \tilde{c}_{44} \alpha_{1} \cosh (\alpha_{1} \eta ),$$
$$\varOmega_{6} = k_{12} \sinh (\alpha_{1} y) - \tilde{c}_{44} \alpha_{1} \cosh (\alpha_{1} y) $$
$$ \varOmega_{7} = k_{12} \cosh (\alpha_{1} y) - \tilde{c}_{44} \alpha_{1} \sinh (\alpha_{1} y),$$
$$\varOmega_{8} = - e^{{2\lambda h_{1} }} \tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} \sinh (\alpha_{2} h_{1} )\sinh (\alpha_{1} h_{3} ) $$
$$ P_{1} = \text{csch} (sh_{2} )\sinh (s\eta ), $$
$$P_{2} = \text{csch} (sh_{2} )\sinh (s(\eta - h_{2} )) $$
Appendix C
$$ {E}_{1} = \text{csch} (h_{2} \alpha_{1} )\{ Q_{1} + \tilde{c}_{44} G_{y} \alpha_{1} [Q_{2} + k_{12} (Q_{3} + k_{13} (Q_{4} + Q_{5} \alpha_{2} ))]\} $$
$$ {E}_{2} = Q_{6} - Q_{7} + \tilde{c}_{44} \alpha_{1} G_{y} (Q_{8} + Q_{9} ) $$
$$ {E}_{3} = \text{csch} (h_{2} \alpha_{1} )[Q_{10} + Q_{11} + k_{13} (Q_{12} + Q_{13} \alpha_{2} )] $$
$$ {E}_{4} = Q_{14} + \tilde{c}_{44} G_{y} \alpha_{1} (Q_{15} + k_{12} (Q_{16} + Q_{17} )) $$
$$ \begin{aligned} {E}_{5} = & - 2{\text{e}}^{{h_{1} \alpha_{2} }} \sinh (h_{1} \alpha_{2} )G_{y}^{2} \left( {g^{2} s^{2} - M_{2}^{2} } \right)T_{5} T_{2} + 2{\text{e}}^{{h_{1} \alpha_{2} }} \tilde{c}_{44} G_{y} ( - {\text{e}}^{{2\lambda h_{1} }} \sinh (h_{3} \alpha_{1} )k_{13} T_{3} T_{2} + \sinh (h_{2} \alpha_{1} )k_{12} T_{5} T_{4} )\alpha_{1} \\ & - 2{\text{e}}^{{2\lambda h_{1} + h_{1} \alpha_{2} }} \sinh (h_{2} \alpha_{1} )\sinh (h_{1} \alpha_{2} )\sinh (h_{3} \alpha_{1} )\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} \\ \end{aligned} $$
$$ {E}_{6} = {\text{e}}^{{ - (3\lambda + \alpha_{2} )h_{1} }} [{\text{e}}^{{2\lambda h_{1} }} k_{13} + G_{y} ( - \lambda + \alpha_{2} )](Q_{18} + \tilde{c}_{44} G_{y} \alpha_{1} (Q_{19} + k_{12} \{ Q_{20} + k_{13} [Q_{21} + 2{\text{e}}^{{h_{1} \lambda }} Q_{22} \alpha_{2} ]\} ))(\beta_{11}^{2} - d_{11} \gamma_{11} )^{5} $$
$$ \begin{aligned} {E}_{7} = & \cosh (\alpha_{1} (h_{1} + h_{3} ))\{ Q_{23} + Q_{24} [Q_{25} + \sinh (h_{2} \alpha_{1} )\tilde{c}_{44} \alpha_{1} Q_{26} ]\} (\beta_{11}^{2} - d_{11} \gamma_{11} )^{5} \\ & + \sinh (\alpha_{1} (h_{1} + h_{3} ))\{ Q_{27} [Q_{28} + \sinh (h_{2} \alpha_{1} )\tilde{c}_{44} \alpha Q_{29} ](\beta_{11}^{2} - d_{11} \gamma_{11} )^{5} + Q_{30} \} \\ \end{aligned} $$
$$ {E}_{8} = \frac{{D_{0} \gamma_{11} - B_{0} \beta_{11} }}{{d_{11} \gamma_{11} - \beta_{11}^{2} }} $$
$$ {E}_{9} = \frac{{ - D_{0} \beta_{11} + B_{0} d_{11} }}{{d_{11} \gamma_{11} - \beta_{11}^{2} }} $$
$$ \begin{aligned} E_{10} = & s( - {\text{e}}^{{\frac{{\alpha_{2} h_{1} }}{2}}} G_{y} k_{12} T_{5} T_{16} + {\text{e}}^{{\lambda h_{1} }} k_{13} ((\sinh (h_{2} \alpha_{1} )\sinh (y\alpha_{2} ) \\ + {\text{e}}^{{\lambda h_{1} }} \sinh (h_{3} \alpha_{1} )\sinh (\alpha_{2} (y + h_{1} ))\tilde{c}_{44} k_{12} \alpha_{1} + G_{y} T_{2} T_{17} ))(\varGamma_{3} B_{0} + \varGamma_{2} D_{0} + \tau_{0} )) \\ \end{aligned} $$
$$ \begin{aligned} E_{11} = - (e^{{2\lambda h_{1} }} \sinh (h_{1} \alpha_{2} )\sinh (h_{2} \alpha_{1} )\sinh (h_{3} \alpha_{1} )\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} + \sinh (h_{1} \alpha_{2} )G_{y}^{2} T_{2} \hfill \\ T_{5} (g^{2} s^{2} - M_{2}^{2} ) + \tilde{c}_{44} G_{y} \alpha_{1} (e^{{2\lambda h_{1} }} \sinh (h_{3} \alpha_{1} )k_{13} T_{2} T_{14} - \sinh (h_{2} \alpha_{1} )k_{12} - T_{5} T_{15} )) \hfill \\ \end{aligned} $$
$$ \begin{aligned} E_{12} = & ( - G_{y} ({\text{e}}^{{\lambda h_{1} }} T_{2} \sinh (\alpha_{2} y)k_{13} - {\text{e}}^{{\frac{{\alpha_{2} h_{1} }}{2}}} \sinh \left( {\alpha_{2} (y + \frac{{h_{1} }}{2}))k_{12} T_{5} } \right)(g^{2} s^{2} - M_{2}^{2} ) \\ \quad + {\text{e}}^{{\lambda h_{1} }} \tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1} (\sinh (h_{2} \alpha_{1} )(T_{12} ) + {\text{e}}^{{\lambda h_{1} }} \sinh (h_{3} \alpha_{1} )(T_{13} )))(\varGamma_{3} B_{0} + \varGamma_{2} D_{0} + \tau_{0} ) \\ \end{aligned} $$
$$ Q_{1} = 2{\text{e}}^{{2\lambda h_{1} + h_{1} \alpha_{2} }} \cosh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )\sinh (h_{1} \alpha_{2} )\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} - 2{\text{e}}^{{h_{1} \alpha_{2} }} \sinh (h_{1} \alpha_{2} )G_{y}^{2} (g^{2} s^{2} - M_{2}^{2} )T_{5} T_{10} $$
$$ Q_{2} = 2{\text{e}}^{{(2\lambda + \alpha_{2} )h_{1} }} \cosh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )\tilde{c}_{44} k_{13} \alpha_{1} T_{3} $$
$$ Q_{3} = - \cosh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )\tilde{c}_{44} \alpha_{1} T_{7} $$
$$ Q_{4} = 2{\text{e}}^{{h_{1} \alpha_{2} }} \lambda \sinh (h_{1} \alpha_{2} )[\cosh (\alpha_{1} y)\cosh (h_{3} \alpha_{1} ) - {\text{e}}^{{2\lambda h_{1} }} \sinh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )] $$
$$ Q_{5} = \{ - 2{\text{e}}^{{(\lambda + \alpha_{2} )h_{1} }} \cosh (\alpha_{1} (y - h_{2} )) + 2{\text{e}}^{{h_{1} \alpha_{2} }} \cosh (\alpha_{2} h_{1} )[\cosh (\alpha_{1} y)\cosh (h_{3} \alpha_{1} ) + {\text{e}}^{{2h_{1} \lambda }} \sinh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )]\} $$
$$ Q_{6} = 2{\text{e}}^{{2\lambda h_{1} + h_{1} \alpha_{2} }} \sinh (h_{1} \alpha_{2} )\sinh (h_{3} \alpha_{1} )\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} $$
$$ Q_{7} = \sinh (h_{1} \alpha_{2} )G_{y}^{2} 2{\text{e}}^{{h_{1} \alpha_{2} }} (g^{2} s^{2} - M_{2}^{2} )T_{5} [\coth (h_{2} \alpha_{1} )k_{12} - \tilde{c}_{44} \alpha_{1} ] $$
$$ Q_{8} = {\text{e}}^{{2\lambda h_{1} }} \sinh (h_{3} \alpha_{1} )k_{13} \tilde{c}_{44} \alpha_{1} [2{\text{e}}^{{h_{1} \alpha_{2} }} \lambda \sinh (\alpha_{2} h_{1} ) - \alpha_{2} \cosh (\alpha_{2} h_{1} )] $$
$$ Q_{9} = k_{12} [ - {\text{e}}^{{2\lambda h_{1} }} \coth (h_{2} \alpha_{1} )\sinh (h_{3} \alpha_{1} )k_{13} T_{3} - T_{5} T_{7} ] $$
$$ Q_{10} = 2{\text{e}}^{{2\lambda h_{1} + h_{1} \alpha_{2} }} \sinh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )\sinh (h_{1} \alpha_{2} )\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} + 2{\text{e}}^{{h_{1} \alpha_{2} }} \sinh (h_{1} \alpha_{2} )G_{y}^{2} (g^{2} s^{2} - M_{2}^{2} )T_{5} T_{11} $$
$$ Q_{11} = \tilde{c}_{44} G_{y} \alpha_{1} (2{\text{e}}^{{(2\lambda + \alpha_{2} )h_{1} }} \sinh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )\tilde{c}_{44} k_{13} \alpha_{1} T_{3} + k_{12} ( - \sinh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )\tilde{c}_{44} \alpha_{1} T_{7} $$
$$ Q_{12} = 2{\text{e}}^{{h_{1} \alpha_{2} }} \lambda \sinh (h_{1} \alpha_{2} )[\sinh (\alpha_{1} y)\cosh (h_{3} \alpha_{1} ) - {\text{e}}^{{2\lambda h_{1} }} \cosh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )] $$
$$ Q_{13} = - 2{\text{e}}^{{(\lambda + \alpha_{2} )h_{1} }} \sinh (\alpha_{1} (y - h_{2} )) + 2{\text{e}}^{{h_{1} \alpha_{2} }} \cosh (\alpha_{2} h_{1} )[\sinh (\alpha_{1} y)\cosh (h_{3} \alpha_{1} ) + {\text{e}}^{{2h_{1} \lambda }} \cosh (\alpha_{1} y)\sinh (h_{3} \alpha_{1} )] $$
$$ Q_{14} = - 2{\text{e}}^{{h_{1} \alpha_{2} }} \sinh (h_{1} \alpha_{2} )G_{y}^{2} (g^{2} s^{2} - M_{2}^{2} )T_{1} T_{2} - 2{\text{e}}^{{2\lambda h_{1} + h_{1} \alpha_{2} }} \cosh (\alpha_{1} h_{1} )\sinh (h_{2} \alpha_{1} )\sinh (h_{1} \alpha_{2} )\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} $$
$$ Q_{15} = - 2{\text{e}}^{{(2\lambda + \alpha_{2} )h_{1} }} \cosh (\alpha_{1} h_{1} )\sinh (h_{2} \alpha_{1} )\tilde{c}_{44} k_{13} \alpha_{1} T_{3} $$
$$ Q_{16} = 2{\text{e}}^{{h_{1} \alpha_{2} }} \cosh (\alpha_{1} h_{1} )\sinh (h_{2} \alpha_{1} )\tilde{c}_{44} \alpha_{1} T_{4} $$
$$ Q_{17} = k_{13} (2{\text{e}}^{{h_{1} \alpha_{2} }} \lambda \sinh (h_{1} \alpha_{2} )T_{8} + [2{\text{e}}^{{(\lambda + \alpha_{2} )h_{1} }} \cosh (\alpha_{1} (h_{1} + h_{3} )) - 2{\text{e}}^{{h_{1} \alpha_{2} }} \sinh (\alpha_{2} h_{1} )T_{9} ]\alpha_{2} ) $$
$$ Q_{18} = - 2{\text{e}}^{{\lambda h_{1} }} \sinh (h_{1} \alpha_{2} )G_{y}^{2} ( - g^{2} s^{2} + M_{2}^{2} )T_{2} T_{6} - 2{\text{e}}^{{3\lambda h_{1} }} \sinh (h_{1} \alpha_{1} )\sinh (h_{2} \alpha_{1} )\sinh (h_{1} \alpha_{2} )\tilde{c}_{44}^{2} k_{12} k_{13} \alpha_{1}^{2} $$
$$ Q_{19} = - 2{\text{e}}^{{3\lambda h_{1} }} \sinh (\alpha_{1} h_{1} )\sinh (h_{2} \alpha_{1} )\tilde{c}_{44} k_{13} \alpha_{1} T_{3} $$
$$ Q_{20} = 2{\text{e}}^{{h_{1} \lambda }} \sinh (\alpha_{1} h_{1} )\sinh (h_{2} \alpha_{1} )\tilde{c}_{44} \alpha_{1} T_{4} $$
$$ Q_{21} = 2{\text{e}}^{{\lambda h_{1} }} \lambda \sinh (h_{1} \alpha_{2} )[{\text{e}}^{{2\lambda h_{1} }} \sinh (\alpha_{1} h_{1} )\cosh (h_{2} \alpha_{1} ) + \cosh (\alpha_{1} h_{1} )\sinh (h_{2} \alpha_{1} )] $$
$$ Q_{22} = {\text{e}}^{{2\lambda h_{1} }} \cosh (h_{2} \alpha_{1} )\cosh (\alpha_{2} h_{1} )\sinh (\alpha_{1} h_{1} ) + \cosh (\alpha_{1} h_{1} )\cosh (\alpha_{2} h_{1} )\sinh (\alpha_{1} h_{2} ) + {\text{e}}^{{h_{1} \lambda }} \sinh (\alpha_{1} (h_{1} + h_{3} )) $$
$$ Q_{23} = 2\cosh (\alpha_{1} h_{1} )k_{13}^{2} \alpha_{2} G_{y} \{ \sinh (h_{2} \alpha_{1} )\tilde{c}_{44} \alpha_{1} [k_{12} + G_{y} (\lambda - \alpha_{2} )] + \cosh (h_{2} \alpha_{1} )G_{y} k_{12} ( - \lambda + \alpha_{2} )\} $$
$$ Q_{24} = 2{\text{e}}^{{ - (2\lambda + \alpha_{2} )h_{1} }} \{ \sinh (\alpha_{1} h_{1} )\tilde{c}_{44} \alpha_{1} [ - {\text{e}}^{{2\lambda h_{1} }} k_{13} + G_{y} (\lambda - \alpha_{2} )] + \cosh (\alpha_{1} h_{1} )G_{y} k_{13} (\lambda - \alpha_{2} )\} $$
$$ Q_{25} = \cosh (h_{2} \alpha_{1} )G_{y} k_{12} [\sinh (h_{1} \alpha_{2} )G_{y} ( - g^{2} s^{2} + M_{2}^{2} ) - {\text{e}}^{{2\lambda h_{1} }} T_{3} k_{13} ] $$
$$ Q_{26} = \{ - \cosh (h_{1} \alpha_{2} )G_{y} (k_{12} + {\text{e}}^{{2\lambda h_{1} }} k_{13} )\alpha_{2} + \sinh (h_{1} \alpha_{2} )\{ {\text{e}}^{{2\lambda h_{1} }} (k_{12} + G_{y} \lambda )k_{13} + G_{y} [ - \lambda k_{12} + G_{y} (g^{2} s^{2} - M_{2}^{2} )]\} $$
$$ Q_{27} = - 2{\text{e}}^{{ - (2\lambda + \alpha_{2} )h_{1} }} \{ \cosh (\alpha_{1} h_{1} )\tilde{c}_{44} \alpha_{1} [ - {\text{e}}^{{2\lambda h_{1} }} k_{13} + G_{y} (\lambda - \alpha_{2} )] + \sinh (\alpha_{1} h_{1} )G_{y} k_{13} (\lambda - \alpha_{2} )\} $$
$$ Q_{28} = \cosh (h_{2} \alpha_{1} )G_{y} k_{12} [\sinh (h_{1} \alpha_{2} )G_{y} (g^{2} s^{2} - M_{2}^{2} ) + {\text{e}}^{{2\lambda h_{1} }} T_{3} k_{13} ] $$
$$ Q_{29} = \sinh (h_{1} \alpha_{2} )[ - {\text{e}}^{{2\lambda h_{1} }} (k_{12} + G_{y} \lambda )k_{13} + G_{y} (\lambda k_{12} - G_{y} (g^{2} s^{2} - M_{2}^{2} ))] + \cosh (h_{1} \alpha_{2} )G_{y} (k_{12} + {\text{e}}^{{2\lambda h_{1} }} k_{13} )\alpha_{2} $$
$$ Q_{30} = - 2\sinh (\alpha_{1} h_{1} )k_{13}^{2} \alpha_{2} G_{y} [\sinh (h_{2} \alpha_{1} )\tilde{c}_{44} \alpha_{1} (k_{12} + G_{y} (\lambda - \alpha_{2} )) + \cosh (h_{2} \alpha_{1} )G_{y} k_{12} ( - \lambda + \alpha_{2} )](\beta_{11}^{2} - d_{11} \gamma_{11} )^{5} $$
$$ T_{1} = \sinh (\alpha_{1} h_{1} )k_{13} + \cosh (\alpha_{1} h_{1} )\tilde{c}_{44} \alpha_{1} $$
$$ T_{2} = \sinh (\alpha_{1} h_{2} )\tilde{c}_{44} \alpha_{1} - \cosh (\alpha_{1} h_{2} )k_{12} $$
$$ T_{3} = \sinh (\alpha_{1} h_{2} )\lambda - \cosh (\alpha_{1} h_{2} )\alpha_{2} $$
$$ T_{4} = \sinh (\alpha_{1} h_{2} )\lambda + \cosh (\alpha_{1} h_{2} )\alpha_{2} $$
$$ T_{5} = \sinh (\alpha_{1} h_{3} )\tilde{c}_{44} \alpha_{1} - \cosh (\alpha_{1} h_{3} )k_{13} $$
$$ T_{6} = - \sinh (\alpha_{1} h_{1} )\tilde{c}_{44} \alpha_{1} - \cosh (\alpha_{1} h_{1} )k_{13} $$
$$ T_{7} = 2{\text{e}}^{{\alpha_{2} h_{1} }} \sinh (\alpha_{2} h_{1} )\lambda + \cosh (\alpha_{2} h_{1} )\alpha_{2} $$
$$ T_{8} = \sinh (\alpha_{1} h_{1} )\sinh (\alpha_{1} h_{2} ) + {\text{e}}^{{2\lambda h_{1} }} \cosh (\alpha_{1} h_{1} )\cosh (\alpha_{1} h_{2} ) $$
$$ T_{9} = - \sinh (\alpha_{1} h_{1} )\sinh (\alpha_{1} h_{2} ) + {\text{e}}^{{2\lambda h_{1} }} \cosh (\alpha_{1} h_{1} )\cosh (\alpha_{1} h_{2} ) $$
$$ T_{10} = \sinh (\alpha_{1} y)k_{12} - \cosh (\alpha_{1} y)\tilde{c}_{44} \alpha_{1} $$
$$ T_{11} = \sinh (\alpha_{1} y)\tilde{c}_{44} \alpha_{1} - \cosh (\alpha_{1} y)k_{12} $$
$$ T_{12} = \lambda \sinh (\alpha_{2} y) - \alpha_{2} \cosh (\alpha_{2} y) $$
$$ T_{13} = \lambda \sinh (\alpha_{2} (y + h_{1} )) - \alpha_{2} \cosh (\alpha_{2} (y + h_{1} )) $$
$$ T_{14} = \lambda \sinh (\alpha_{2} h_{1} ) - \alpha_{2} \cosh (\alpha_{2} h_{1} ) $$
$$ T_{15} = \alpha_{2} \cosh (\alpha_{2} h_{1} ) + \lambda \sinh (\alpha_{2} h_{1} ) $$
$$ T_{16} = \alpha_{2} \cosh \left( {\alpha_{2} \left( {y + \frac{{h_{1} }}{2}} \right)) + \lambda \sinh (\alpha_{2} \left( {y + \frac{{h_{1} }}{2}} \right)} \right) $$
$$ T_{17} = \lambda \sinh (\alpha_{2} y) + \alpha_{2} \cosh (\alpha_{2} y) $$
