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A new shear deformation shell theory for free vibration analysis of FG sandwich shells
Omar Slimani,Zakaria Belabed,Fodil Hammadi,Noureddine Taibi,Abdelouahed Tounsi 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.78 No.6
In recent years, many researches have been published dealing with the mechanical responses of shells with variable cross-sectional mechanical properties such as sandwich, functionally graded and laminated composites shells. In the present paper, a simple and efficient shear deformation theory is formulated for the free vibration response of functionally graded sandwich shells. The main advantage of this theory is its reduced number of unknowns and their related governing equations and theses tend to be highly compared to others shear deformation shell theories. Two kinds of FG sandwich shells are studied with respect to their geometrical configuration and material properties. The first kind is composed of FG facesheet and homogeneous core and the other is formed by homogeneous facesheet and FG core. The governing equations of motion for the free vibration analysis are obtained using Hamilton’s principle. The closed form solutions are sought by using the Navier’s method for eigenvalue problems. The accuracy and efficiency of the present theory are established and proved by comparing obtained numerical results with those predicted by other higher order shear deformation shell theories. The influences of various parameters such as material distribution, thickness of the core and the facesheet of sandwich shell and curvature ratios are studied, discussed and reported as significant rate sensitivity to predict the fundamental frequencies of FG sandwich shells.
Zakaria Belabed,Mahmoud M. Selim,Omar Slimani,Noureddine Taibi,Abdelouahed Tounsi,Muzamal Hussain 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.40 No.2
In this study, a simple and efficient higher order shear deformation theory is formulated for free vibration analysis of functionally graded (FG) shells. By introducing the undetermined integral terms in displacement field, the number of generated unknowns and their related governing equations is reduced in contrast to previously published theories, and therefore the differentiability of governing motion equations is decreased , this motivation turns the present theory simpler and easily exploited for functionally graded shell mechanical simulation. Both strains and stress rise through the thickness coordinate as function of hyperbolical distribution. The Hamilton’s principle is deployed to derive the governing and motion equations. Closed form solutions are obtained for free vibration problems using Navier’s method. Furthermore, detailed comparisons with other shear deformation theories are presented to illustrate the efficiency and accuracy of the developed theory. From this perspective, various perceptions on the impact of some important parameters such as material distribution, geometrical configuration, thickness and curvature ratios are studied and discussed. The non-trivial aspects in predicting the free vibration responses of FG shells are also pointed out.