Analysis of a Nonlinear Aeroelastic System with Parametric Uncertainties Using Polynomial Chaos Expansion

Table 1

$\langle {\mathrm{\Phi }}_1{\mathrm{\Phi }}_1\rangle =1$	$\langle {\mathrm{\Phi }}_0{\mathrm{\Phi }}_0{\mathrm{\Phi }}_0{\mathrm{\Phi }}_0{\mathrm{\Phi }}_0\rangle =1$
$\langle {\mathrm{\Phi }}_2{\mathrm{\Phi }}_2\rangle =2$	$\langle {\mathrm{\Phi }}_0{\mathrm{\Phi }}_0{\mathrm{\Phi }}_1{\mathrm{\Phi }}_1{\mathrm{\Phi }}_2\rangle =2$
$\langle {\mathrm{\Phi }}_3{\mathrm{\Phi }}_3\rangle =6$	$\langle {\mathrm{\Phi }}_0{\mathrm{\Phi }}_1{\mathrm{\Phi }}_1{\mathrm{\Phi }}_2{\mathrm{\Phi }}_2\rangle =10$
$\langle {\mathrm{\Phi }}_4{\mathrm{\Phi }}_4\rangle =24$	$\langle {\mathrm{\Phi }}_0{\mathrm{\Phi }}_1{\mathrm{\Phi }}_2{\mathrm{\Phi }}_2{\mathrm{\Phi }}_3\rangle =48$