Aeroelastic reliability and sensitivity analysis of a plate interacting with stochastic axial airflow

Abstract

The aeroelastic reliability and sensitivity of a simply supported isotropic plate interacting with upper axial airflow are investigated. Based on the assumed mode method and the linear potential flow theory, the equation of motion of the plate interacting with axial airflow is established using the Hamilton’s principle. The limit state function representing the aeroelastic failure mode is obtained from aerodynamic stability analysis of the plate. The mean value first order second moment method is adopted to analyze the aeroelastic reliability and sensitivity of the plate. The effects of the stochastic properties of the flow velocity, flow density, and the plate geometry dimensions on the aeroelastic reliability are analyzed. From the results, it can be seen that the aeroelastic reliability decreases with increasing velocity and mass density of the airflow. The flow mass density has more significant effects on the reliability sensitivity than the flow velocity. The reliability decreases with increasing length and width, and increases with increasing thickness of the plate. The standard deviation of the thickness of the plate has more significant effects on the aeroelastic reliability than the length and width. This study provides a new perspective on understanding the instability behaviors of the plate in airflow.

Appendix

$$\begin{aligned} \mathbf{K}_1= & {} \int _0^b {\int _0^a {\frac{Eh}{2(1-\nu ^{2})}\frac{\partial \mathbf{U}}{\partial x}\frac{\partial \mathbf{U}^{\mathrm{T}}}{\partial x}+\frac{Eh}{4(1+\nu )}\frac{\partial \mathbf{U}}{\partial y}\frac{\partial \mathbf{U}^{\mathrm{T}}}{\partial y}dxdy} }\end{aligned}$$

(A-1)

$$\begin{aligned} \mathbf{K}_2= & {} \int _0^b {\int _0^a {\frac{Eh}{2(1-\nu ^{2})}\frac{\partial \mathbf{V}}{\partial y}\frac{\partial \mathbf{V}^{\hbox {T}}}{\partial y}+\frac{Eh}{4(1+\nu )}\frac{\partial \mathbf{V}}{\partial x}\frac{\partial \mathbf{V}^{\mathrm{T}}}{\partial x}dxdy} }\end{aligned}$$

(A-2)

$$\begin{aligned} \mathbf{K}_3= & {} \int _0^b \int _0^a \frac{Eh^{3}}{12(1-\nu ^{2})}\left[ \nu \frac{\partial ^{2}{} \mathbf{W}}{\partial x^{2}}\frac{\partial ^{2}\mathbf{W}^{\mathrm{T}}}{\partial y^{2}}+\frac{1}{2}\left( \frac{\partial ^{2}\mathbf{W}}{\partial x^{2}}\frac{\partial ^{2}{} \mathbf{W}^{\mathrm{T}}}{\partial x^{2}}\right. \right. \nonumber \\&\left. +\frac{\partial ^{2}{} \mathbf{W}}{\partial y^{2}}\frac{\partial ^{2}{} \mathbf{W}^\mathrm{T}}{\partial y^{2}}\right) +\left( 1-\nu \right) \frac{\partial ^{2}{} \mathbf{W}}{\partial x\partial y}\left. \frac{\partial ^{2}{} \mathbf{W}^{\mathrm{T}}}{\partial x\partial y}\right] dxdy\end{aligned}$$

(A-3)

$$\begin{aligned} \mathbf{K}_4= & {} \int _0^b {\int _0^a {\frac{\nu Eh}{(1-\nu ^{2})}\frac{\partial \mathbf{U}}{\partial x}\frac{\partial \mathbf{V}^{\mathrm{T}}}{\partial y}+\frac{Eh}{2(1+\nu )}\frac{\partial \mathbf{V}}{\partial x}\frac{\partial \mathbf{U}^{\mathrm{T}}}{\partial y}dxdy} }\end{aligned}$$

(A-4)

$$\begin{aligned} \mathbf{M}_1= & {} \int _0^b {\int _0^a {\rho h\mathbf{UU}^{\mathrm{T}}dxdy} } , \quad \mathbf{M}_2 =\int _0^b {\int _0^a {\rho h\mathbf{VV}^{\mathrm{T}}dxdy} } , \nonumber \\ \mathbf{M}_3= & {} \int _0^b {\int _0^a {\rho h\mathbf{WW}^{\mathrm{T}}dxdy}}\end{aligned}$$

(A-5)

$$\begin{aligned} \mathbf{M}_f= & {} \int _0^b {\int _0^a {\rho _\infty {\tilde{\mathbf{W}}{} \mathbf{W}}^{\mathrm{T}}dxdy} } ,\end{aligned}$$

(A-6)

$$\begin{aligned} \mathbf{C}_f= & {} \int _0^b {\int _0^a {2\rho _\infty U_\infty \frac{\partial {\tilde{\mathbf{W}}}}{\partial x}{} \mathbf{W}^{\mathrm{T}}dxdy} } ,\end{aligned}$$

(A-7)

$$\begin{aligned} \mathbf{K}_f= & {} \int _0^b {\int _0^a {\rho _\infty U_\infty ^2 \frac{\partial ^{2}{\tilde{\mathbf{W}}}}{\partial x^{2}}\mathbf{W}^{\mathrm{T}}dxdy} } \end{aligned}$$

(A-8)