Finite Element Analysis, Ground Vibration Testing, and Characterization of Vibration Modes for a Cantilever Plate Representing an Aircraft Wing With and Without Secondary Structure Attached

One of the most critical testing procedures for an airplane certification is Ground Vibration Testing (GVT). With proper GVT analysts can determine the stiffness distribution, natural frequencies, mode shapes and structural damping of each airplane components, which are needed for flutter and dynamic loads analyses. Hence, the results from GVT are crucial. The problem identified in this study is focused on structural design, which can lead to catastrophic situations, if proper attention is not given to GVT results. In GVT, analysts attempt to instrument most of the primary components of the airplane while often neglecting secondary structures such as bungees, gears, control surfaces, etc. These secondary structures must also be considered during GVT in identifying the in-phase and out-of-phase modes in order to achieve higher accuracy when tuning the stiffness of the primary structure. During the stiffness tuning process for the flutter analysis, tuning the primary structure stiffness to in-phase torsion mode can be considered as a conservative approach and will require design change. Conversely, if the stiffness of the primary structure is tuned to out-of-phase torsion mode, which is always higher, the analysis becomes unconservative. The goal of this study is to reconstruct the above-mentioned problem of in-phase and out-of-phase vibration modes of a cantilever plate with an attached secondary structure, replicating a simple model of aircraft wing structure. This includes performing the modal experiments and finite element analysis (FEA) of a cantilever plate (primary structure) with and without flexible links (secondary structure) attached to the plate and characterizing the in-phase and out-of-phase modes of the flexible links. A thorough study using frequency response functions (FRFs) is performed to characterize the modes using different accelerometer ‘raw data’ readings measured from different locations on the dynamic system. For GVT of the cantilever plate, natural frequencies associated with the respective mode shapes are identified and calculated and a comparison is made between the test results, the FEA results, and from an analytical approach. A parametric study is then conducted to evaluate and quantify the change in the frequencies of the in-phase and out-of-phase modes with the change in the chord-wise and span-wise location of the flexible attachment of the secondary structure to the primary structure, and due to the change in the compliant stiffness of the flexible link to the plate. Proper identification and correlation of the modes and natural frequencies of the cantilever plate with and without the secondary structure are presented. It is concluded that the in-phase and out-of-phase torsion frequencies increased with higher compliant stiffness. With the chord-wise change in location of the flexible link, both the in-phase and out-of-phase frequencies increased when the center of gravity of the link move towards the center of the chord from both leading and trailing edges of the plate. With the span-wise change in CG of the link, the in-phase frequency reduced with span (i.e., when the CG moves away from the constraint location of the plate) and the out-of-phase frequency increased.