I think in applying boundary condition for pressure on the surface of an oscillating airfoil in an inviscid flow Du/Dt for fluid particle can not be calculated by differentiating u(t)(u(t) is airfoil motion) because of slip condition on airfoil surface.

You have to apply the tangent flow boundary condition along with the boundary condition on the pressure ( dp/dn=-rho*du/dt dot n ) where u is the structural velocity vector and n is the normal vector.