Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

Abstract

The search for ever lighter weight has become a major goal in the aeronautical industry as it has a direct impact on fuel consumption. It also implies the design of increasingly thin structures made of sophisticated and flexible materials. This may result in nonlinear behaviours due to large structural displacements. Stator vanes can be affected by such phenomena, and as they are a critical part of turbojets, it is crucial to predict these behaviours during the design process in order to eliminate them. This paper presents a reduced order modelling process suited for the study of geometric nonlinearities. The method is derived from a classical Component Mode Synthesis with fixed interfaces, in which the reduced nonlinear terms are obtained through a STEP procedure using an adapted basis composed of linear modes completed by modal derivatives. The whole system is solved using a harmonic balance procedure and a classic iterative nonlinear solver. The application is implemented on a schematic stator vane model composed of nonlinear Euler-Bernoulli beams under von Kàrmàn assumptions.

Nonlinear Harmonic Analysis of a Blade Model Subjected to Large Geometrical Deflection and Internal Resonance

“…The study presented in this document has been conducted on a significantly reduced model, however this paper highlights the potential of the described methods to predict internal resonance phenomena for an industrial model with the harmonic balance method. In further works, it would be interesting to complete the reduction basis using, for instance, modal derivatives [25].…”

Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities

“…Such a construction requires the use of a vector basis for projecting the nonlinear computational model. Many methods can be used for constructing such vector basis, see for instance [41,42,30,43,29].…”

“…It should be noted that the effects of nonlinearities on the dynamics have been considered by [27] for a simple generic cyclic structure exhibiting nonlinear stiffness connections (and not for nonlinear geometrical effects, and furthermore, without mistuning). The effects of geometrical nonlinearities using the Harmonic Balance Method have been analyzed by [28,29] for tuned bladed disks (with neither mistuning nor detuning). The first work concerning the effects of nonlinear geometrical effects of mistuned bladed disk based on a probabilistic model without detuning can be found in [30].…”

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

“…Applications to real-world engineering problems are numerous and tend to increase since lightweight thinner structures are being increasingly used. The range of applications thus spans from aeronautics to transportation industry [114,163,179,216,224,226,232,271], wind energy systems [74,160], musical instruments [30,106,184] and micro-/nanoelectromechanical systems (M/NEMS), in which those nonlinearities must be mastered to design efficient structures [61,138,164,245,322]. The vibratory phenomena arising from the nonlinear dynamics of geometrically nonlinear structures can also be intentionally used for the purpose of new designs, especially in the M/NEMS domain or for energy harvesting, where for example internal resonances or parametric driving are conceived with specific goals [58,96,148,157,231,248,258,270,319].…”