Maxime Peeters

Modal Analysis of a Nonlinear Periodic Structure with Cyclic Symmetry

This paper carries out modal analysis of a nonlinear periodic structure with cyclic symme- try. The nonlinear normal mode (NNM) theory is brie°y described, and a computational algorithm for the NNM computation is presented. The results obtained on a simpli¯ed model of a bladed assembly show that this system possesses a very complicated struc- ture of NNMs, including similar and nonsimilar NNMs, nonlocalized and localized NNMs, bifurcating and internally resonant NNMs. Modal interactions that occur without neces- sarily having commensurate natural frequencies in the underlying linear system are also discussed.

Nonlinear Normal Modes of a Full-Scale Aircraft

The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft, whose ground vibration tests have exhibited some nonlinear structural behaviors. The finite element model of this aircraft, elaborated from drawings, has more than 80000 degrees of freedom, and softening nonlinearities exist in the connection between the external fuel tanks and the wing tips. From this model, a reduced-order model, which is accurate in the [0-100Hz] range, is constructed using the Craig-Bampton technique. The NNMs of the reduced model are then computed using a numerical algorithm combining shooting and pseudo-arclength continuation. The results show that the NNMs of this full-scale structure can be computed accurately even in strongly nonlinear regimes and with a reasonable computational burden. Nonlinear modal interactions are also highlighted by the algorithm and are discussed.

Energy Transfer and Dissipation in a Duffing Oscillator Coupled to a Nonlinear Attachment

The dynamics of a two-degree-of-freedom nonlinear system consisting of a grounded Duffing oscillator coupled to an essentially nonlinear attachment is examined in the present study. The underlying Hamiltonian system is first considered, and its nonlinear normal modes are computed using numerical continuation and gathered in a frequency-energy plot. Based on these results, the damped system is then considered, and the basic mechanisms for energy transfer and dissipation are analyzed.

Phase resonance testing of nonlinear vibrating structures

Modal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single NNM during the experiments, similarly to what is carried out for ground vibration testing. With the help of time-frequency analysis, NNM modal curves and their frequencies are then extracted from the time series. The proposed methodology is demonstrated using a simple numerical benchmark, which consists of a two-degree-offreedom system with a cubic spring.

Nonlinear modal analysis and energy localization in a bladed disk assembly

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedure and a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequency-energy dependence of nonlinear oscillations.Copyright

Modal Testing of Nonlinear Vibrating Structures Based on a Nonlinear Extension of Force Appropriation

Modal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is investigated in this study in order to isolate one single NNM during the experiments, similarly to what is carried out for ground vibration testing. With the help of time-frequency analysis, the modal curves and the corresponding backbones are then extracted from the time series. The proposed methodology is demonstrated using a numerical benchmark, which consists of a planar cantilever beam with a cubic spring at its free end.Copyright

Localization of energy in a perfectly symmetric bladed disk assembly due to nonlinearities

Although a bladed disk is typically designed to have identical blades, manufacturing tolerances, wear, and other causes may cause random deviations among the blades. The blade-to-blade discrepancies, denoted as mistuning, lead to vibratory responses mostly concentrated in small regions of the bladed-disk assembly, according to a phenomenon called localization. The resulting spatial confinement of the vibration energy causes the responses of some blades to become dangerously high and increases the amplitude of the bladed-disk assembly’s overall response. The attendant increase in stresses can lead to premature high cycle fatigue (HCF) of the blades. In this study we investigate whether vibration localization in a perfectly symmetric bladed disk assembly may occur in the presence of nonlinearity. To this end, the nonlinear normal modes (NNMs) of a simplified model of a bladed disk assembly are computed. The NNMs are then carefully examined to highlight possible vibration localization phenomena.Copyright

Theoretical and Experimental Modal Analysis of Nonlinear Aerospace Structures

Because nonlinearity is a frequent occurrence in aerospace applications, there is a need for ecien t analysis procedures. In this context, nonlinear normal modes (NNMs) oer a solid mathematical tool for interpreting a wide class of nonlinear dynamical phenomena. The objective of this study is to highlight the usefulness of NNMs for modeling and testing of nonlinear aerospace structures. Both theoretical and experimental modal analysis are described and are illustrated.