Optical Characterization of a Pendular Impact

Abstract

We present a simple but accurate correlation between an experimental characterization and a simple analytical prediction of a wave propagation induced by the impact of a pendulum in a box filled with fine sand; this research is based on optical measurements and was carried out using the digital image correlation technique to determine the motion on the surface of the box visually observed by the reflection of the laser. We suggest that the reaction to the impact in the body will be similar to an equivalent damped mass-spring system, obtaining an average error of 3.67208 × 10 −4 .

Optical Analysis of the Impact Transmission in Steel Sheet Arrays with Bolted-Type Joints

“…Years later, the authors announced another analytical approach by solving a damping mass-spring system, in which a damped wave was obtained as a solution. Again, the experimental results evidenced downward movement [8].…”

“…According to the analytical solutions shown in [7][8][9], first, the authors declared a sum of two waves as the first analytical approximation to the motion recorded experimentally. This solution gave them an accuracy of 92%.…”

“…where C c is the mathematical correlation. Normalization is performed, stating M as the image size and s 1 and s 2 as the standard deviation of the images corresponding to [8,9]. Equation ( 2) gives a matrix-type result; thus, the maximum amplitude point was logically defined.…”

“…It is part of the intensity field I in (1), and it is related to the real and imaginary part of the complex amplitude of each speckle [32]. As this is an iterative process, from the second to the n image, those peak amplitudes are plotted as scalar values measured in millimeters according to [8,9].…”

“…Then, the authors normalized the action-reaction impact by means of a pendulum. The collision response was modeled with an equivalent damped mass-spring system [8]. Finally, an approximation to a modeled wing was handled, in which impacts were subjected to a rigid body, but reactions were measured in an embedded bar.…”