Sandwich-plate vibration analysis: Three-layer quasi-three-dimensional finite element model

Abstract

A three-layer finite element model for the vibration analysis of sandwich plates with laminated composite face sheets is evaluated. In the model the face sheets are represented as Reissner-Mindlin plates, and the core is modeled as a three-dimensional continuum. This representation allows accurate modeling for a wide range of core types. The three-dimensional problem is reduced to two dimensions by analytical through-thickness integration of the energy expressions for the evaluation of mass and stiffness matrices. The results from this model are compared to finite element results based on solid elements, classical sandwich analysis, and classical plate theory. The objective in the work is to compare natural frequency and mode shape predictions using these models for a broad range of core stiffness. When large differences between face sheet and core stiffness are present, it is illustrated that traditional laminate theories yield significant inaccuracy. Moreover, unlike plate models, the present theory is also capable of representing a variety of three-dimensional boundary conditions. Furthermore, compared to solid models, the present laminated model avoids numerical problems as a result of three-dimensional element aspect ratio. Therefore, the present model provides a powerful general tool for the analysis of natural modes and frequencies of sandwich plates.