Abstract Three-dimensional scanning laser vibrome- ters enable extremely accurate non-contact measure- ment of the three-dimensional displacements on the surface of structures。 This paper looks at the feasibility of using such a scanning laser vibrometer for the non- contact measurement of dynamic strain fields across the surface of a planar structure subjected to in-plane loading。 Issues such as laser head alignment and choice of differentiation filter parameters are discussed。 Fi- nally, experimental results of two test specimens are presented which clearly demonstrate the significant po- tential of this new experimental technique as well as highlighting several limitations。83932

Keywords  3D laser scanning vibrometry ·Displacement · Strain · Optical measurements

LRT4 - Institute of Mechanics, Universität der Bundeswehr München, 85577 Neubiberg, Germany Introduction The measurement of displacement, strain and stress fields is important in many areas of applied mechanics and engineering。 Such measurements are most com- monly conducted by contact techniques using strain gauges or piezo-electric sensors, or non-contact meth- ods such as digital image correlation [1], speckle inter- ferometry [2], photo-elasticity [3], x-ray diffraction [4] and holographic interferometry [5]。83932

The development of laser vibrometry measurement systems stimulated the application of scanning laser vibrometers to measure the out-of-plane displacement in plate- or shell-like structures, from which the curva- ture, bending strain and stresses may be estimated via a double spatial derivative [6–8]。 Due to poor transducer quality, early applications of the laser vibrometer tech- nique required extensive spatial filtering to improve the quality of the strain estimates, at the expense of spatial resolution。

Recently 3D laser vibrometers have entered the market, which allow the non-contact (remote) mea- surement of not only the out-of-plane displacement component, but also the in-plane displacement com- ponents。 These vibrometers are comprised of three laser heads slaved together such that all three laser beams are focused on to a single measurement point, which can be moved in unison via mirrors connected to servo motors。 The scanning function allows automated sequential measurement of the vibration at a number of predefined points or grid。 The three laser heads directly measure velocities (or displacements) in three dimensions at each measurement point, from which displacements in the three spatial directions may be evaluated。

In an insightful paper on the application on 3D laser vibrometry, Mitchell et al。 [9] suggested that ‘with the full-surface response descriptions one can consider the development of strain distributions over the surface’。 This is opposed to all published work to date that used a single laser head to measure out-of-plane displace- ment, and therefore only enabled bending strain to be determined。 It took almost an entire decade before Mitchell’s vision became a reality in which 3D laser vi- brometry was demonstrated to estimate strain [10, 11]。 According to the manufacturer of the Polytec PSV-3D, three-dimensional measurement of dynamic surface strain has only been possible in the last few years with the availability of 3D scanning laser vibrometers with sufficient spatial resolution and the associated high res- olution decoders。 With the introduction of online trian- gulation software and high resolution video cameras ac- curate strain estimates from 3D vibrometers is possible。 In this paper, the application of a Polytec 3D scan- ning laser vibrometer (PSV-3D) to the measurement of the kinematic variables is presented for three isotropic plate structures; a uniform rectangular plate, a rectan- gular plate with a concentric hole and a rectangular plate with a side-crack。 The underlying theory of the laser vibrometer and strain theory is initially discussed, followed by a series of experiments used to test the approach。 A quasi-static loading regime is employed to enable comparison with results from a two-dimensional model computed using Ansys , a commercial finite- element software package。 Techniques for removing noise from the experimental data are  presented  in this paper。 The displacements are temporally aver- aged using Fourier analysis and spatially filtered using the Saviztky–Golay filter [12]。 This filter is adapted to provide the spatial derivatives necessary for strain calculation (a technique successfully employed by Pan et al。 [13] for strain estimation in digital image corre- lation)。 Advantages and limitations of the strain detec- tion technique via scanning laser vibrometry are  also