Natural element hierarchic models for the free vibration analyses of laminate composite plates

Abstract

The conventional theories like CLPT, FSDT and HSDT used for the structural analyses of single or laminate composite structures are characterized by the type and order of thickness-wise displacement functions. Based upon this fact, a family of hierarchic models is developed, as a unified theory, for the free vibration analysis of laminate composite plates. The displacement field is expressed by the product of the 2-D in-plane unknown functions and the 1-D thickness-wise monomials. The model level is identified by the maximum order of thickness-wise monomial, and the corresponding hierarchic model is derived according to the equivalent single layer theory. The hierarchic models are numerically implemented by applying 2-D natural element method (NEM) to the in-plane displacement functions that are defined on the midsurface of laminate composite structures. The hierarchic models are illustrated through the numerical experiments and their major characteristics are examined to the model level and the structure thickness. Furthermore, the reliability of proposed hierarchic models is assessed from the comparison with the representative classical theories. The numerical results justify that the natural element hierarchic models (NEHM) can effectively analyze the free vibration analysis of laminate composite plates.