Construction of digital shadow moire images for the analysis of bending vibrations of a plate

Abstract

The problem of bending vibrations is common in different engineering and physical applications. Bending vibrations of centrally clamped rotating circular disks play crucial role in functionality of hard disk drives. Lots of efforts are spent for dynamic stabilization, control and measurement of bending vibrations in such micromechanical systems. Nevertheless, measurement of microscopic deflections from the state of equilibrium is a challenging problem. Different optical measurement techniques are developed for experimental investigation of bending vibrations. Shadow moire is one of the popular methods for experimental analysis of bending vibrations of structures. Unfortunately, interpretation of experimental measurement results is a nontrivial inverse engineering problem often having non-unique solutions. Therefore there exists a definite need for hybrid numerical -experimental techniques that could help to interpret the measurement results. The procedure for the generation of digital stroboscopic shadow moiré images for the eigenmodes of bending vibrations of a plate is developed. It is based on the methods of computer graphics and the method of finite elements for the analysis of bending vibrations of a plate. The construction of digital shadow moire images builds the ground for hybrid numerical-experimental procedures and enables to analyze the experimental results with greater precision.