A fundamental issue in turbomachinery design is the dynamical stress assessment of turbine blades. In order to reduce stress peaks in the turbine blades at engine orders corresponding to blade natural frequencies, friction dampers are employed. Blade response calculation requires the solution of a set of non-linear equations originated by the introduction of friction damping.
Such a set of non-linear equations is solved using the iterative numerical Newton–Raphson method. However, calculation of the Jacobian matrix of the system using classical numerical finite difference schemes makes frequency domain solver prohibitively expensive for structures with many contact points. Large computation time results from the evaluation of partial derivatives of the non-linear equations with respect to the displacements.
In this work a methodology to compute efficiently the Jacobian matrix of a dynamic system having wedge dampers is presented. It is exact and completely analytical.
The proposed methods have been successfully applied to a real intermediate pressure turbine (IPT) blade under cyclic symmetry boundary conditions with underplatform wedge dampers. Its implementation showed to be very effective, and allowed to achieve relevant time savings without loss of precision. 相似文献
We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters. 相似文献