Modal analysis of hyperelastic structures in non-trivial equilibrium states via higher-order plate finite elements

The present work proposes a higher-order plate finite element model for the three-dimensional modal analysis of hyperelastic structures. Refined higher-order 2D models are defined in the well-established Carrera Unified Formulation (CUF) framework, coupled with the classical hyperelastic constitutive law modeling based on the strain energy function approach. Matrix forms of governing equations for static nonlinear analysis and modal analysis around nontrivial equilibrium conditions are carried out using the Principle of Virtual Displacements (PVD). The primary investigation of the following study is about the natural frequencies and modal shapes exhibited by hyperelastic soft structures subjected to pre-stress conditions.