Nonlinear modal analysis of aerospace structures

The dynamic systems theory is well-established for linear systems and can rely on mature tools such as the theories of linear operators and linear integral transforms. This is why theoretical and experimental modal analysis, i.e., the computation of vibration modes from a mathematical model and from experimental data, respectively, is really quite sophisticated and advanced. Even though linear modal analysis served, and is still serving, the structural dynamics community for applications ranging from bridges to satellites, it is commonly accepted that nonlinearity is a frequent occurrence in engineering structures. Because linear modal analysis fails in the presence of nonlinear dynamical phenomena, the development of a practical nonlinear analog of modal analysis would be an extremely timely contribution; it is clearly missing in the structural dynamics literature. A new framework for nonlinear modal analysis of real-world structures, which includes the computation of nonlinear modes from finite element models, is introduced in this paper. This framework will permit a rigorous, yet understandable by the practicing engineer, analysis of nonlinear dynamical phenomena. It will also provide solid theoretical foundations for extending finite element model validation to nonlinear aerospace structures.

[1]  Alexander F. Vakakis,et al.  Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment , 2005 .

[2]  Peter Eberhard,et al.  Sensitivity analysis for dynamic mechanical systems with finite rotations , 2008 .

[3]  Yu. A. Kuznetsov,et al.  Applied nonlinear dynamics: Analytical, computational, and experimental methods , 1996 .

[4]  Alexander F. Vakakis,et al.  Normal modes and localization in nonlinear systems , 1996 .

[5]  Eric Pesheck,et al.  Reduced order modeling of nonlinear structural systems using nonlinear normal modes and invariant manifolds , 2000 .

[6]  Alexander F. Vakakis,et al.  Nonlinear normal modes, Part I: A useful framework for the structural dynamicist , 2009 .

[7]  C. J. Hartwigsena,et al.  Experimental study of non-linear effects in a typical shear lap joint configuration , 2004 .

[8]  Sami F. Masri,et al.  A Nonparametric Identification Technique for Nonlinear Dynamic Problems , 1979 .

[9]  Gaëtan Kerschen,et al.  Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques , 2009 .

[10]  L. Gaul,et al.  Nonlinear dynamics of structures assembled by bolted joints , 1997 .

[11]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[12]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[13]  R. Seydel.  Practical Bifurcation and Stability Analysis , 1994 .

[14]  D. M. McFarland,et al.  Experimental study of non-linear effects in a typical shear lap joint configuration , 2004 .

[15]  Alexander F. Vakakis,et al.  NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW , 1997 .

[16]  Bruno Cochelin,et al.  Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes , 2006 .

[17]  Marco Amabili,et al.  Reduced-order models for large-amplitude vibrations of shells including in-plane inertia , 2008 .

[18]  Joseph C. Slater,et al.  A numerical method for determining nonlinear normal modes , 1996 .