Fig。 2 Three sensor heads and high resolution camera (centre) of the PSV-400-3D laser scanning  vibrometer

Fig。 3 Testing apparatus

30 kN and the pulling force, that is relevant for the measurements, can reach a maximum value of 3,500 N。 The specimens are made from the transparent ther- moplastic polymethyl methacrylate (PMMA), which is also known as acrylic。 The acrylic sheet has a nominal thickness of 2 mm。 The length and the width of the specimens equal 215 mm and 92 mm, respectively。 The geometry is specified in Fig。 4, where the clamped areas are shaded grey。 The notches at the upper and    lower

ends of the specimen were necessary to fit around the bolts used to tighten the clamps。

To evaluate the strain measurements via a scanning laser vibrometer, an undamaged plate and a plate with a circular hole with a radius of r = 10 mm were inves- tigated。 The undamaged plate can be seen mounted to the testing apparatus in Fig。 3。

As mentioned in the introduction, the loading (de- tailed further in Section “Measurement Scheme”) was quasi-static in order allow comparison of the exper- imental results and static two-dimensional finite ele- ment models computed using Ansys 。 It should be noted that measurements could have been conducted above the stiffness control regime (at or above the fun- damental resonance) however direct comparison with the finite element model becomes considerably more difficult due to uncertainty in damping and natural frequencies。

Preparation of the Measurement

Prior to conducting measurements, the laser heads have to be aligned to each other and to the measurement object。 Firstly, a 3D alignment is conducted to deter- mine the distances and the angles between the lasers。 For this purpose an alignment sample (PSV-A-450) with measurements points in different planes with a defined distance to each other is utilized。 After which the alignment sample is replaced by the specimen and a 2D alignment is carried out。 This defines the distance between the sensor heads and the specimen。 The accu- racy of the laser position achieved with the alignment reported in this paper was 0。1 mm, 0。1 mm and 0。3 mm for the top laser, the left laser and the right laser, respectively。

The acrylic samples are transparent and hence the light would be transmitted through the surface instead of being reflected to the sensor heads。 To obtain a nontransparent and opaque surface the specimens are treated with a solvent based developer (Ardrox 9D1B)。 This suspension of an inert white powder in a quick dying solvent leaves a white opaque surface。 This en- hances the intensity of the laser light that is reflected towards the sensor heads。

Measurement Scheme

Several different loading frequencies were investigated。 However, the possible frequency range of the exci- tation was very limited with the given setup, as the first resonance frequency of the testing apparatus was 7 Hz, and some hysteresis between the voltage   input

for the piezo actuator and the load signal from the load cell was observed at frequencies above 3 Hz。 In an attempt to increase the quality of the measurements, the specimens were excited at several tones (all be- low 7 Hz) simultaneously。 An averaged signal for a multi-tone excitement did not show any improvement compared to a single tone excitement。 Thereupon, a sinusoidal loading frequency of 1 Hz was chosen for the all measurements, which corresponds to loading in the stiffness controlled region where the strains and applied load are in phase。 Pretension of the specimen assured tensional load only。 The measurements were carried out in the frequency domain。 The phase shift between the applied force measured by the load cell and the displacement field measured by the vibrometer for the measured frequency was less than 1◦。 The input voltage for the piezo stack actuator was utilized as a reference signal so that the phase information could be obtained from the transfer functions between the primary and the reference signal。 For a given load the amplitude of the velocities is recorded and hence the results presented refer to strain and stress amplitudes。