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Many analytical solutions and experimental techniques have been developed which attempt to characterize the dynamics of a structure. In this study, the dynamics of the structure under test are characterized by the spatial representation of the energy flowing through the structure. The spatial representation of the energy or power flow may be used to define the flow of energy from the energy sources to sinks. Conceptually, once the energy path in the structure can be characterized, the structure can be designed to channel or dissipate energy to meet design goals. This concept is analogous to designing the load path of a structure in static design. In order to obtain an accurate spatial model of the power flow and determine points of energy sources and sinks, a high spatial density of the structure response is required. It is impractical to obtain a high spatial density of the response with the use of accelerometers or other structurally mounted measuring devices. In this experimental approach, a scanning laser Doppler vibrometer (LDV) acquires data used in developing a spatial three dimensional model of the steady-state dynamic response. The system response is represented by the three-dimensional complex valued velocity field. From this experimentally derived spatial dynamics model, an accurate representation of the structure's actual energy and power flow can be extracted. In this research, the underlying assumptions in the analytical methods of power flow for beams are discussed and their effects are quantified. A scanning LDV is used to make velocity measurements by scanning the entire beam structure from multiple scan positions. The experimental spatial dynamics modeling technique is used to solve for the three-dimensional complex velocity field of the vibrating beam. From this spatial representation of the dynamic response, the components of power flow due to the shear force and the bending moment are extracted and used to determine the total power flow along the beam. With the methods presented in this paper, a spatial model of the experimental energy and power flow can be determined.
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