Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores

Abstract

This paper dealt with free vibration analysis of thick double curved composite sandwich panels with simply supported or fully clamped boundary conditions based on a new improved higher order sandwich panel theory. The formulation used the first order shear deformation theory for composite face sheets and polynomial description for the displacement field in the core layer which was based on the displacement field of Frostig's second model. The fully dynamic effects of the core layer and face sheets were also considered in this study. Using the Hamilton's principle, the governing equations were derived. Moreover, effects of some important parameters like that of boundary conditions, thickness ratio of the core to panel, radii curvatures and composite lay-up sequences were investigated on free vibration response of the panel. The results were validated by those published in the literature and with the FE results obtained by ABAQUS software. It was shown that thicker panels with a thicker core provided greater resistance to resonant vibrations. Also, effect of increasing the core thickness in general was significant decreased fundamental natural frequency values. KeywordsFree vibration, Double curved sandwich panel, Boundary conditions, Improved higher order sandwich panel theory.Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores INTRODUCTIONStructural efficiency is an important attribute for aircraft structures. A higher order theory approach, used by Kant and Patil (1991), replaced sandwich structure with an equivalent higher order shear deformable structure, which lacked the ability to determine local buckling modes and imperfection effects on the overall behavior. Using the three-dimensional elasticity equations, Bhimaraddi (1993) studied the static response of orthotropic doubly curved shallow shells. He assumed that the ratio of the shell thickness to its middle surface radius is negligible as compared to unity. The high- er order sandwich panel theory was developed by Frostig et al. (1994Frostig et al. ( , 2004, who considered two types of computational models in order to express governing equations of the core layer. The second model assumed a polynomial description of the displacement fields in the core that was based on displacement fields of the first model. Their theory did not impose any restrictions on distribution of the deformation through thickness of the core. Singh (1999) studied free vibration of the open deep sandwich shells made of thin layers and a moderately thick core. Rayleigh-Ritz method was also used to obtain natural frequencies. The improved higher order sandwich plate theory (IHSAPT), applying the first-order shear deformation theory for the face sheets, was introduced by Malekzadeh et al. (2005Malekzadeh et al. ( , 2006.

On buckling and free vibration studies of sandwich plates and cylindrical shells: A review

“…250 A very general free vibration analysis of thick double-curved composite sandwich panels with simply supported or fully clamped boundary conditions based on a new improved higher order sandwich panel theory. 251 The free vibration analysis of simply supported cross-ply laminated composite and sandwich doubly-curved shells is presented based on HSDTs. 252 Zigzag function is implemented to introduce discontinuity at the core/faces interfaces to build HOTs to evaluate the free vibration response of sandwich plates and shells with soft cores.…”

An efficient general curvilinear coordinates finite element method for the linear dynamic study of thickness-independent shells

“…The pioneering work of Reddy and Liu (1985), who developed a 2-D higher-order theory for laminated elastic shells accounting for a parabolic distribution of the transverse shear strains through the thickness of the shell and tangential stress-free boundary conditions on the boundary surface of the shell, was the starting point for a series of theories which try to reproduce the behavior of thick shells, especially in the case of high frequencies. In this regard, Fard et al (2014) presents a good review of different variants of the finite element method which study this problem and proposes an improved higher order double curved sandwich shell theory to analyze the free vibrations of double curved thick composite sandwich panels. In addition, they considered the terms �1 + �, corresponding to the components of the mixed curvature tensor expressed in orthogonal coordinates, and integrated them exactly through the thickness.…”

Experimental and numerical analysis of vibration frequency in sandwich composites with different radii of curvature

“…Most studies cited in literature were conducted on flat sandwich panels. However, very limited knowledge exists on vibration behavior of curved sandwich panels [17,18]. The free vibration of doubly curved composite honeycomb sandwich panels was investigated by Cunningham et al.…”