Variable stiffness (VS) panels are gaining popularity in the field of aerospace applications. The possibility of tailoring the elastic properties is indeed an effective way to improve buckling, postbuckling and free vibration behaviors, as shown by previous works in the literature [1,2,3].Relatively less attention has been devoted in the past to the address the potential offered by VS designs to improve the vibration response in the nonlinear field. This aspect is of interest for aerospace panels, which are sometimes required to operate under nonlinear conditions promoted by large amplitude vibrations [4]. Previous works referred to the finite element method [3], yet its application can be time-consuming, especially when repeated nonlinear analyses are required, such as in the case of preliminary assessments or design optimizations.This paper presents a fast approach for the analysis of VS composite plates, i.e. plates with non-uniform elastic properties along the in-plane direction. The formulation relies upon third-order shear deformation theory, which allows thin and relatively thick plates to be analyzed. A mixed variational theorem is applied as underlying theoretical framework, leading to a straightforward formulation of the problem. For efficiency, the spatial discretization is performed by means of the Ritz method, where the unknowns are expanded via Legendre polynomials and boundary functions. Due to their excellent convergence properties, few degrees of freedom are generally sufficient, rendering the computational procedure particularly efficient.Different approaches are proposed for solving the resulting set of nonlinear ordinary differential equations in the time variable: direct integration, differential quadrature method (DQM) and an arc-length continuation technique based on the harmonic balance method (HBM). To keep at minimum the time for the analysis, simplified closed-form solutions are derived as well.The goal of this paper is twofold. Firstly, presenting a comparison between the different solution procedures, both in terms of time for the analysis, as well as accuracy of the predictions. Different test cases are presented for this scope, and the comparison against reference results is discussed. Excellent accuracy is revealed both in the case of thin and moderately thick plates. The time for the analysis, depending on the solution strategy, can be as low as few fractions of a second. 
Secondly, the efficiency of the proposed formulations is exploited to perform parametric studies on VS panels. The potential of elastic tailoring is investigated by addressing the effects of different design variables, e.g. fiber orientations at different locations, on the nonlinear vibration responses. The results indicate that the nonlinear response can be shaped through proper design of the internal load paths, demonstrating potential advantages offered by a VS design over a straight-fiber one.References1. Z. Wu, P.M. Weaver, G. Raju, and B.C. Kim. Buckling analysis and optimisation of variable angle tow composite plates. Thin-Walled Structures, 60:163–172, 2012.2. R. Vescovini, E. Spigarolo, E. Jansen, and L. Dozio. Efficient post-buckling analysis of variable-stiffness plates using a perturbation approach. Thin-Walled Structures, 143:106211, 2019.3. H. Akhavan, P. Ribeiro, and M.F.S.F. De Moura. Large deflection and stresses in variable stiffness composite laminates with curvilinear fibres. International Journal of Mechanical Sciences, 73:14–26, 2013.4. M. Amabili. Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press, 2008.

Fast Methods for Nonlinear Vibration Analysis of Variable Stiffness Panels

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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