No abstract

A laser technique which measures vibrational energy flow (intensity) via propagating bending waves is described. A pair of scanning laser beams from a two-channel laser vibrometer is used to provide a nonintrusive measurement of the intensity at various points on a vibrating beam. Results are shown to compare well with those of two additional techniques. These techniques, used for validation, employ a single laser beam and can only be used at resonance frequencies in beams or rods. The two-channel laser technique described can be applied to two-dimensional intensity measurements, is not limited to single frequency excitation, and has an inherent capability to facilitate phase error elimination via a photodetector switching technique which is also described.

In laser Doppler vibrometry of sinusoidal vibration, direct analysis of the photodetector output or the heterodyne signal using a spectrum analyzer is emphasized. A technique utilizing the spectra at the carrier frequency and the first sideband is proposed for unambiguous analysis of the vibration amplitude. Experimental results demonstrate the validity of the proposed technique.Subject terms: laser Doppler vibrometry; heterodyne detection; vibration analysis; spectrum analysis.Optical Engineering 28 (8), 922 -925 (August 1989).

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.

This paper extends the application of a two-channel vibrometer technique from the measurement of flexural energy flow (detailed in Part 1) to the measurement of longitudinal energy flow. The two-channel longitudinal energy flow equations and two one-dimensional validation methods are presented along with a discussion of how laser vibrometry functions for the measurement of in-plane vibratory motion. Adaptations of the energy flow equations to laser vibrometry are also presented. Experimental results are illustrated which contain the influence of a bending-induced longitudinal component of motion. Through a mathematical model, the measurement of the longitudinal energy flow is shown to be accurate if the influence of bending-induced longitudinal motion is removed.