40 E. Delhez et al. Steel strip Massm Fixation x z y Fu Fw w t Lateral guide Mass ZOOM Fig. 7.1 Schematic view of the experimental set-up first passage time of such systems. The existence of these regimes for the average first passage time have been demonstrated experimentally in [3]. This paper focuses on the study of the second order moment of the first passage time. 7.2 Experimental Set-Up Description The experimental set-up is represented in a schematic way in Fig. 7.1. It consists in a vertical strip pre-stressed by a mass m=1.816 kg. The strip is characterized by a length =0.501 m, a width w =25 mm and a thickness t =0.4mm. The structure is made of steel (Young’s modulus E=206 GPa and densityρ =7767kg/m3). It is clamped at its top end. A lateral guide at the bottom end constrains the strip to move only in the vertical direction. The forced and parametric excitations Fw and Fu are applied by means of two shakers. The first shaker is mounted horizontally and is used to excite the strip out of its plane. This force constitutes the forced excitation. The second shaker is mounted vertically at the bottom of the structure. This force modifies the pre-stress load of the strip, giving rise to the parametric excitation. A picture of the physical prototype of the structure with the two shakers is given in Fig. 7.2. Using an appropriate scaling [3], this problem can be cast into a dimensionless format similar to Eq. (7.1). 7.3 Numerical Modelling The strip itself is modelled in MATLAB using Bernoulli beam elements. Stiffness in rotation about the y-axis is experimentally identified and introduced at both extremities of the strip to reflect the actual boundary conditions. The horizontal shaker, the stinger and the impedance head glued to the strip are modeled by a spring-mass system. The influence of the impedance head is also taken into account by increasing the stiffness of the finite elements in contact with the transducer. The different parameters of the model are tuned to minimize (in a least square sense) the difference between the natural frequencies obtained with the numerical model and those identified experimentally with the “Least Square Complex Exponential” and “Least Square Frequency Domain” methods [3].
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