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In this paper we consider the algebra of two‐point tensors on manifolds. A new way to define transposition is suggested. Further, we consider orthogonal two‐point tensors. Finally, we investigate symmetry of two‐point and ordinary tensors. We demonstrate applications of our results to examples from nonlinear solid mechanics.

Impulse mistuning is an alternative approach for the reduction of vibration stresses of blades and vanes. In contrast to most other approaches it is not a direct energy dissipation approach but a mistuning based one. However, the approach is not aimed at making use of the geometrical mistuning of the structure (e.g. a blade or a vane stage). Mistuners, specially designed small bodies are placed at specific locations inside of the component e.g. of a blade or of a vane. They do not directly dissipate enough energy to cause relevant damping like a friction or friction-impact damper, because of the small mass involved, but rather mistune the eigen frequencies of the structure using impulses (impacts). As a result, the structure absorbs less energy at the original resonance and hence answers with lower vibration amplitude. In fact, impulse mistuning is a special case of absorption — the so called Targeted Energy Transfer (TET) with “Vibro-Impact Nonlinear Energy Sinks” (VI-NES) — with very small impact mass involved and thus a negligible role of dissipation while experiencing a significant amount of absorption. The energy will be transferred (or “pumped”) to other resonances, sometimes outside of the primary resonance crossing and partially dissipated. We use the names “impulse mistuning” or “mistuners” instead of TET or VI-NES because (in our opinion) it better describes the physics of this special kind of absorption. In the paper, the design and validation of two impulse mistuning systems, for a blade stage and a vane cluster of a lower power turbine, are presented.

Since the first nonlinear forced response validation of frictionally coupled bladed disks, more than 20 years have passed, and numerous incremental modeling and simulation refinements were proposed. With the present work, we intend to assess how much we have improved since then. To this end, we present findings of an exhaustive validation campaign designed to systematically validate the nonlinear vibration prediction for the different friction joints at blade roots, interlocked shrouds and under-platform dampers. An original approach for the identification of crucial contact properties is developed. By using the dynamic Lagrangian contact formulation and a refined spatial contact discretization, it is demonstrated that the delicate identification of contact stiffness properties can be circumvented. The friction coefficient is measured in a separate test, and determined as unique function of temperature, preload, wear state. Rotating rig and engine measurements are compared against simulations with the tool OrAgL, developed jointly by the Leibniz Universität Hannover and the University of Stuttgart, in which state-of-the-art component mode synthesis (CMS) and harmonic balance methods (HBMs) are implemented.