The aeroelastic stability of turbomachinery blade assemblies is usually assessed numerically on isolated blade row configurations although upstream/downstream blade rows can significantly alter the stability. We consider in this paper the influence of a neighboring blade row to compute the generalized aerodynamic forces from which the aeroelastic damping can be evaluated. For that purpose we resort to phase-shifted boundary conditions in the numerical model of a single passage of each blade row to take into account the multiple unsteady phenomena induced by the blade vibration, the blade passage effect of the adjacent blade row and their possible interaction. A Fourier approximation of the global generalized aerodynamic forces of the whole blade is then proposed using the local generalized aerodynamic forces computed on the single blade modeled. An analytic expression of the aeroelastic damping computed with the energy method is finally proposed and the results are compared to those obtained from full annulus reference computations in which all passages are modeled.