FRF Measurements and Mode Shapes Determined Using Image-based 3D Point-tracking Chris Warren, Chris Niezrecki, Peter Avitabile Structural Dynamics and Acoustic Systems Laboratory University of Massachusetts Lowell One University Avenue Lowell, Massachusetts 01854 ABSTRACT Today, accelerometers and laser Doppler vibrometers are widely accepted as valid measurement tools for structural dynamic measurements. However, limitations of these transducers prevent the accurate measurement of some phenomena. For example, accelerometers typically measure motion at a limited number of discrete points and can mass load a structure. Scanning laser vibrometers have a very wide frequency range and can measure many points without mass-loading, but are sensitive to large displacements and can have lengthy acquisition times due to sequential measurements. Image-based stereophotogrammetry techniques provide additional measurement capabilities that compliment the current array of measurement systems by providing an alternative that favors high-displacement and low-frequency vibrations typically difficult to measure with accelerometers and laser vibrometers. Within this paper, displacements determined using 3D pointtracking are used to calculate frequency response functions, from which mode shapes are extracted. The image-based frequency response functions (FRFs) are compared to those obtained at collocated accelerometers. Mode shapes are then compared to a previously validated finite element model (FEM) and are shown to have excellent agreement between the FEM and the conventional measurement approaches when compared using the Modal Assurance Criterion (MAC) and PseudoOrthogonality Check (POC). INTRODUCTION With the advent of digital cameras, image-based point-tracking is becoming a more common method to track the motion of optical targets that are attached to a rigid or flexible body. To date, 3D point-tracking (3DPT) has not been validated within the field of structural dynamics as a non-contacting vibration measurement tool. When evaluating the performance of any new system or technique, one must compare the new approach to existing measurement methods or to analytical solutions. To accomplish this end, a well documented and understood test article was chosen to compare the image-based approach to established measurement techniques. A structure known as the “Base-Upright” (BU) has been used in a number of studies and was chosen for its well-known dynamic characteristics [1-4]. Several test setups were needed to study the BU, depending on the measurement system and transducers used. A summary of past work using accelerometers, laser Doppler vibrometers, and slow-speed cameras is presented, followed by a thorough discussion of the setup and results of tests run with high-speed cameras. Finally, conclusions are drawn to highlight the strengths and weaknesses of 3D point-tracking using high-speed cameras relative to the other measurement techniques. Description of the Test Article and Finite Element Model The BU was designed to be a structure with well-spaced, directional modes that could be identified easily. Figure 1a shows the BU with the primary dimensions labeled. The base plate is 24 x 24 inches in dimension and rigidly bolted to the concrete laboratory floor at four locations, while the upright is 24 x 30 inches in dimension. Both plates are made from 3/4” thick aluminum and are bolted together by two steel angle brackets. A finite element model (FEM) is available and has been shown to be very well correlated to other measured test data from previous studies [1-4]. The FEM was assembled with solid elements and has approximately 58,000 degrees of freedom (DOF). For reference, the analytical frequencies and mode shapes for the first 8 modes are shown in Figure 1b. T. Proulx (ed.), Modal Analysis Topics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series 6, 243 DOI 10.1007/978-1-4419-9299-4_20, © The Society for Experimental Mechanics, Inc. 2011
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