Applications of VAM-based homogenization model in free and forced vibrations of sandwich plates with bowtie-shaped auxetic core

Abstract

To investigate the dynamic characteristics of composite sandwich plates (CSPs) with bowtie-shaped auxetic cores (bowtie CSPs), a two-dimensional homogenization plate model (2D-HPM) was developed using variational asymptotic method (VAM). The novelty is that the equivalent stiffness is obtained by homogenizing the typical unit cell, and is input into the 2D-HPM for free and forced vibration analysis. The accuracy of the 2D-HPM and the equivalent stiffnesses were verified by comparison with the results of the three-dimensional finite element model (3D-FEM). The effects of the negative Poisson’s ratio (NPR), layup configurations, and geometric parameters on the equivalent stiffness and dynamic characteristics of the bowtie CSP are discussed and compared with the results of sandwich plates with re-entrant or honeycomb cores. The comparison results showed that the bowtie CSP had lower natural frequencies due to the NPR effect. The dynamic characteristics of the bowtie CSP were closely related to the geometric size of the core cell and layup configurations of the facesheets. Furthermore, the 2D-HPM significantly improved the calculation efficiency while ensuring the accuracies of natural frequency and time-/frequency-domain response. The tailoring of unit cells in the present model provides a useful reference for the structural dynamic optimization of bowtie CSPs.