Abstract
The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.
Highlights
Shells are structural elements commonly employed by engineers, architects and designers to fulfil particular structural requirements
The main aim of the present paper is to investigate the natural frequencies of shell structures with variable thickness made of Functionally Graded Materials (FGMs)
The four structures with variable thickness made of FGMs depicted in Figure 4 are considered in the present section to evaluate their natural frequencies by the Local Generalized Differential Quadrature (LGDQ) method
Summary
Shells are structural elements commonly employed by engineers, architects and designers to fulfil particular structural requirements. Due to their peculiar shape and the curvature effect they are characterized by high-level stiffness, which allows to carry external loads in an efficient way Their dynamic behavior is considerably affected by these curved geometries. It is evident that their importance is well-known in many fields, such as automotive, mechanical, civil, and aerospace engineering, architecture, aeronautical and naval industries [1,2,3]. Assessment of their advantages due to the curvature effect are made difficult by lack of accurate analytical description of
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