For the dynamic response of multilayer sheet structures it is important to take nonlinear contact and friction forces between the layers into account. The nonlinearities inside the joints can significantly influence the dynamic behavior of the entire structure. For the dynamic analysis of such structures conventional computational approaches have an unbalanced ratio between computational time and accuracy. In order to overcome this problem, so-called “Joint Interface Modes” (JIMs) are used. These JIMs, which are problem-oriented trial vectors, extend the reduction base of classical trial vector based reduction methods. In this contribution a new calculation approach for JIMs based on trial vector derivatives is introduced. The result quality of the presented method is comparable to the direct finite element method but the computational effort is extremely low due to model order reduction.