A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is achieved subject to parameter uncertainties. The practicability of the approach regarding the extensive amount of required design evaluations is strictly related to the computational efficiency of the nonlinear dynamic analysis. Therefore, it is proposed to employ a recently developed parametric reduced order model (ROM) based on nonlinear modes of vibration, which can facilitate a decrease of the computational burden by several orders of magnitude. The approach was applied to a rotationally periodic assembly of a bladed disk with underplatform friction dampers. The robustness of the optimum damper design was significantly improved compared to the deterministic approach, taking into account uncertainties in the friction coefficient, the excitation level and the linear damping. Moreover, a scale invariance for piecewise linear contact constraints is proven, which can be very useful for the reduction of the numerical effort for the analysis of such systems.
Technical applications with unilateral contact are often modeled as multiple coupled discrete mass points. The transition between contact states is often described by transforming the contact formulation into a linear complementary problem (LCP). In case of compliant materials such as rubber, the LCP can be simplified so that no algorithm is needed to solve the equation system. Thus, computational effort can be reduced considerably. In this paper a windscreen wiper lip is modeled as a simple mechanical system with unilateral contact points. The system consists of masses which are coupled by linear springs and dampers. The masses can come into contact with a rigid surface. The equations of motion are derived and transformed into an LCP. The modeling of the coupled, compliant system leads to a simplification of the equation system. Therefore, it can be solved line by line as single independent scalar LCP’s. Also at the transition from separation to contact, when an impact occurs, the contact points can be considered individually. It will be shown, that the coupling can be neglected during the infinitesimal small time of impact. The LCP formulation in combination with simple models of compliant structures therefore yields an effective method for treating multibody systems or discretized continua with several unilateral contact points.
Freestanding turbine blades have typically low structural damping and thus require additional friction damping devices, such as underplatform dampers. The friction coupling between neighboring blades reduces response amplitude and increases resonance frequency. Along with forced response excitation large blades, especially of last stage, could be excited by fluid structural interaction (flutter). To prevent such excitation alternate mistuned blade patterns are beneficial disturbing traveling waves in the stage.
In this paper the influence of alternate mistuning is investigated with a simplified oscillator chain as well as a bladed disk assembly coupled by frictional contacts. It is pointed out that the performance of friction coupling can be improved by alternate mistuning as long as the engine order of the excitation is below quarter of the number of blades. Alternate mistuning causes a mode coupling between two nodal diameter vibration mode shapes allowing for energy transfer. The in-house developed software code DATAR is enhanced and alternate mistuning can be applied to the blades as well as to the damping elements. For validation the DATAR code was applied to an alternate mistuned last stage blade of a Siemens gas turbine and compared with available field engine measurement.
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