RIGID BODY MODES LOW FREQUENCY FLEXIBLE MODES HIGH FREQUENCY MODES LARGE NDOF FEM VERY DETAILED FEM > @ a2 U > @ a1 U > @ a3 U > @ > @ > @ > @ > @ n HF LF RB U U U U > @ > @> @ g LF a2 uT U U > @ > @> @ g a1 RB uT U U > @ > @> @ g HF a3 uT U U Figure 2 – Schematic of Overall Reduction/Expansion/Merging of Hybrid Sets of Data MODEL DESCRIPTION AND CASES STUDIED The beam consisted of a 50” long rectangular tubular cross section beam 3/16” thick with two 3 1/2” x 5” x 3/8” thick flanges. A finite element model was developed using FEMAP [8] to generate the mesh and then processed using FEMTools [9] software package for the eigensolution as well as correlation to all the different data sets. The model consisted of 1000 elements and 1337 nodes to describe the system; the system was analyzed in a free free condition and only planar motion about the weaker beam axis was considered for the studies performed for this demonstration. The mode shapes are typical as would be expected for this simple structure. The experimental planar modes of the beam were obtained in three separate tests - one for the rigid body modes, one for the low frequency flexible modes, and one for the higher frequency flexible modes. Rigid Body Modes The beam response was measured using an optical measurement system using digital image correlation and dynamic photogrammetry with the Aramis/Pontos system [10, 11]. Impact excitation was performed to measure the response at many locations. However, for the studies in this paper only 6 measurement locations were chosen to describe the rigid body motion. Frequency response functions were obtained from processing the time data captured from the optically measured data; additional information on the collection and processing of this type of data can be found in previous studies [12]. Two low frequency rigid body modes were extracted from the data – a bounce mode and a rocking mode as expected. Low Frequency Flexible Modes The beam response was measured using traditional accelerometers for the low frequency flexible modes of the system. These measurements can be obtained from either shaker tests or from impact tests; shaker excitation using burst random was used to extract the response. The frequency response functions were collected at 15 measurement locations over a span of 1000 Hz and modal data was extracted using conventional approaches available in LMS Test.LAB [13]. The first three flexible modes of the structure were extracted and were typical of the expected mode shapes for these modes. 168
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