THE EXTRACTION OF LONGITUDINAL STRAIN FIELDS FROM THE DYNAMIC RESPONSE OF A VIBRATING BEAM

摘要

This paper reports on an initial formulation and results of a research project to extract the longitudinal strain field from the dynamic response of a vibrating beam using the concepts of laser based structural imaging. As the scanning laser vibrometer makes high spatial density measurement of the dynamic response on the structure, the reconstruction of the steady-state velocity field is possible. Given the steady-state velocity amplitude, the displacement field and strain fields can be determined. The overall goal of this research is to investigate the extraction of the strain field from the steady-state velocity field over a vibrating beam structure from laser data. An existing formulation based on the cubic finite element representation is used for reconstructing the steady-state velocity field over the vibrating beam. The formulation presented assumes linear dynamics and a harmonic forcing function which allows the displacement field to be derived from the steady-state velocity field. The formulation of the strain field is developed assuming Euler-Bernoulli beam theory as the underlying mechanics. The resulting strain field derived from the technique is compared against analytical strain results.