Experimental identification of the bending stiffness and damping of plates using the frequency-adapted virtual fields Method

Inverse vibroacoustic methods can be used to identify the complex bending stiffness of a plate from its vibratory response. This work focuses on the Virtual Fields Method (VFM) and the Force Analysis Technique (FAT). The VFM uses functions called virtual fields to solve the Principle of Virtual Work, a weak form of equilibrium, and identifies complex bending stiffness. Here, the virtual fields are defined as piecewise functions over a surface smaller than the plate (virtual window). FAT uses a finite-difference scheme to discretize the fourth-order spatial derivatives of the displacement in the local equilibrium of the plate and thus estimates the bending stiffness. The application of a finite-difference scheme creates a bias in the identified stiffness, which increases with frequency. The Corrected Force Analysis Technique (CFAT) corrects this bias in the high-frequency domain. In this study, it is proposed to apply the CFAT principles to the VFM to adapt the method, using the virtual window size, so it can be applied it in the high-frequency domain. FAT, CFAT, the VFM and the Frequency-Adapted VFM will be presented. The method was tested on experimental data to identify the complex bending stiffness of an aluminium plate partially covered with a damping material.