  In this paper, a generalization of a quadratic manifold approach for the
reduction of geometrically nonlinear structural dynamics problems is presented.
This generalization is constructed by a linearization of the static force with
respect to the generalized coordinates, resulting in a shift of the quadratic
behavior from the force to the manifold. In this framework, static derivatives
emerge as natural extensions to modal derivatives for displacement fields other
than the vibration modes, such as the Krylov subspace vectors. Here the dynamic
problem is projected onto the tangent space of the quadratic manifold, allowing
for a much less number of generalized coordinates compared to linear basis
methods. The potential of the quadratic manifold approach is investigated in a
numerical study, where several variations of the approach are compared on
different examples, indicating a clear pattern where the proposed approach is
applicable.
