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\begin{document}
\[\frac{\partial (N_{11}-N_1^T)R}{\partial z_1}+\frac{\partial N_{21}}{\partial z_2}-\bar{k}\frac{\partial u_1^2}{\partial t^2}-\bar{J}\frac{\partial \phi_1^2}{\partial t^2}+c_1k_4R \frac{\partial (\frac{\partial u_3^2}{\partial z_2})}{\partial z_2}+R(1+\frac{h}{2R})q_1=0\]

\begin{equation*}
\begin{cases}
N_1^T=\int_{-\frac{h}{2}}^{\frac{h}{2}}(-\beta \Delta T)~ dz_3 ~\delta \varepsilon_{11}^0 \\
\frac{\delta \varepsilon_{11}^0}{\partial z_1}=\sum(-Jk_{1z}^2)\bar{e}u_{1n}
\end{cases}
\end{equation*}
با تبدیل سری داریم:
\begin{align*}
& + \frac{1}{R}\Big[\bar{k} \omega^2 R-n^2A_{66}'' -k_{1z}^2R^2A_{11} +N_1^Tk_{1z}^2R^2\Big]U_{1n}\\
& -\Big[\frac{nk_{1z}}{R}(C_1(E _{12}+E_{66})+RA_{12}+RA_{66})\Big]U_{2n}\\
& -\Big[\frac{k_{1z}}{R}(RA_{12}+C_1(k_{1z}^2 . R^2 E_{11}+n^2(E_{12}+E_{66}+E_{66}'')+R^2\omega^2 k_4))\Big]U_{3n}\\
& +\Big[\frac{1}{R}(\bar{J}R\omega^2-n^2B_{66}''+n^2C_1E_{66}''-k_{1z}^2B_{11}+C_1k_{1z}^2E_{11}) \Big]\phi_{1n} \\
& -\Big[ nk_{1z}(B_12-C_1E_{12}+B_{66}-C_1E_{66})\Big] \phi_{2n}=0
\end{align*}
 معادله‌ی 24)  
 \\
 معادله‌ی 26)
 \begin{align*}
 &C_1R\Big(\frac{\partial^2 P_{11}}{\partial z_1^2}-\frac{\partial^2 }{\partial z_1^2}P_2^T\Big)-(N_{22}-N_2^T)+\frac{C_1}{R}\frac{\partial^2 }{\partial z_1^2}(P_{22}-P_2^T)+C_1(\frac{\partial^2 P_{12}}{\partial z_1 \partial z_2}+\Big(\frac{\partial^2 P_{21}}{\partial z_1 \partial z_2}\Big)+ \\
 &+R \frac{\partial \phi_{23}}{\partial z_1}+\frac{\partial \phi_{23}}{\partial z_2}-3C_1\Big( R\frac{\partial R_{13}}{\partial z_1}+\frac{\partial R_{23}}{\partial z_2}\Big)-\frac{2C_1}{R}\frac{\partial P_{23}}{\partial z_2}-C_1W_4 \frac{\partial u''_2}{\partial z_2}-C_1J s\frac{\partial u''_2}{\partial z_2} \\
 & -C_1Rk_4 \frac{\partial u''_1}{\partial z_1} -C_1RJs \frac{\partial \phi_2 ''}{\partial z_1}-RI_1\frac{\partial^2 u_3}{\partial t^2}+C_1^2I_7R\Big( \frac{\partial^2 u''_3}{\partial z_1^2}+\frac{1}{R^2}\frac{\partial^2 u''_3}{\partial z_2^2}\Big)+R(1+\frac{h}{2R})q_3=0
 \end{align*}


\begin{equation*}
[-C_1RE_{11}k_{1z}^3-A_{21}k_{1z}-\frac{C_1}{R}E_{21}k_{1z}n^2-\frac{C_1}{R} E_{66}n^2 k_{1z}+C_1R \omega^2 k_4 k_{1z} -\frac{C_1}{R}E''_{66}n^2k_{1z}]U_{1n}
\end{equation*}
\begin{align*}
&-\Big( \frac{1}{R^3}\Big) n \Big[R^2(A_{22}+A_{44})+RC_1(-R^2\omega^2 W_4-6RD_{44}+R^2k_{1z}^2E_{21}+E_{22}+n^2E_{22}) \\
& -4E_{44}+R^2k_{1z}^2(E'_{66}+E_{66})+C_1^2(9R^2E_{44}+12RG_{44}+R^2k_{1z}^2H_{12}+\\
& +n^2H_{22}+4H_{44}+R^2k_{1z}^2(H_{66}+H'_{66}))-N_2^TR^2-C_1^2P_2^Tn^2\Big]U_{2n}
\end{align*}

\begin{align*}
&(-C_1^2 RH_{11}k_{1z}^4-C_1E_{12}k_{1z}^2-\frac{C_1^2}{R}H_{12}n^2k_{1z}^2+C_1^2RP_1^Tk_{1z}^4-\frac{C_1}{R^2}E_{22}.n^2\\
& -\frac{1}{R}A_{22}-C_1 E_{21}k_{1z}^2+\frac{1}{R} .N_2^T-\frac{C_1^2}{R} H_{21}k_{1z}^2n^2-\frac{C_1}{R^2}E_{22}n^2-\frac{C_1^2}{R^3}H_{22}n^4\\
& \textsc{h} \textsf{h} \textsl{h}\texttt{h}
\end{align*}
\end{document}