Power flow in coupled bending and longitudinal waves in beams

In complex structures, curvature and impedance discontinuities (e.g., junctions) couple bending and longitudinal waves. Propagation losses for longitudinal waves are often much less than losses for bending waves, and damping treatments often less effective on longitudinal waves. When the dissipation in longitudinal waves is less than that on bending waves, longitudinal waves can provide an efficient means of power flow between bending waves generated at one location and bending waves that are a source of acoustic radiation at another location. In order to design and locate effective treatments, knowledge of the power flow in longitudinal as well as bending waves is required. The measurement of power in both bending and longitudinal waves when both waves are present is demonstrated. Measurements conducted on a straight beam and a T-beam are compared to predictions obtained using finite element methods. The effect of coupling between waves at the junction in a T-beam is illustrated using results from measurements of power flow.