An analytical formulation for the vectors of contact forces and the stiffness matrix of the nonlinear friction contact interface Is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed disks. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation

Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark–Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. The HB method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device.

The present review article addresses the vibration behavior of bladed disks encountered e.g. in aircraft engines as well as industrial gas and steam turbines. The utilization of the dissipative effects of dry friction in mechanical joints is a common means of the passive mitigation of structural vibrations caused by aeroelastic excitation mechanisms. The prediction of the vibration behavior is a scientific challenge due to (a) the strongly nonlinear contact interactions involving local sticking, sliding and liftoff, (b) the model order required to accurately describe the dynamic behavior of the assembly, and (c) the multi-disciplinary character of the problem associated with the need to account for structural mechanical as well as fluid dynamical effects. The purpose of this article is the overview and discussion the current state of the art of vibration prediction approaches. The modeling approaches in this work embrace the description of the rotating bladed disk, the contact modeling, the consideration of aeroelastic effects, appropriate model order reduction techniques and the exploitation of the rotationally periodic nature of the problem. The simulation approaches cover the direct computation of periodic, steady-state externally forced and self-excited vibrations using the high-order harmonic balance method, the formulation of the contact problem in the frequency domain, methods for the solution of the governing algebraic equations and advanced simulation approaches, including the concept of nonlinear modes.

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Vibration Prediction of Bladed Disks Coupled by Friction Joints

Complex non-linear modal analysis for mechanical systems : Application to turbomachinery bladings with friction interfaces

A multiharmonic method for analysis of non-linear dynamic systems submitted to periodic loading conditions is presented. The approach is based on a systematic use of the fast Fourier transform. The exact linearization of the resulting equations in the frequency domain allows to obtain full quadratic convergence rate

Albert Lerusse

Papers

A multiharmonic method for non‐linear vibration analysis