Free vibration analysis of homogeneous piezoelectric structures using specific hexahedral elements with rotational DOFs

This paper deals with the free vibration validation of a family of mechanical and piezoelectric eight-node hexahedral elements, presenting rotational degrees of freedom in addition to the classical displacement ones. Their formulations are based on the 3D virtual rotations of a nodal fiber within the finite element that enriches the mechanical displacement vector, stiffness and mass matrices approximations. The performances of these elements for free vibration problems are assessed by means of several beam, plate and shell modal tests, and their results are compared with analytical, experimental and numerical reference solutions. In particular, it is shown that these elements are well adapted for evaluating the modal response of thin and thick elastic and piezoelectric structures, and their accuracy is close to those of the classical mechanical and piezoelectric 20-node hexahedral elements.