Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

Abstract

Due to some technical issues that can appear during the manufacturing process of Functionally Graded Materials (FGMs), it can be extremely difficult to produce perfect materials. Indeed, one of the biggest problems is the presence of porosities. For this purpose, the vibrational behavior of doubly-curved shells made of FGM including porosities is investigated in this paper. With respect to previous research, the porosity has been added to the mechanical model that characterizes the through-the-thickness distribution of the graded constituents and applied to doubly-curved shell structures. Few papers have been published on this topic. In fact, it is easier to find works related to one-dimensional structures and beam models that take account the effect of porosities. The First-order Shear Deformation Theory (FSDT) is considered as the theoretical framework. In addition, the mechanical properties of the constituents vary along the thickness direction. For this purpose, two power-law distributions are employed to characterize their volume fraction. Strain components are established in an orthogonal curvilinear coordinate system and the governing equations are derived according to the Hamilton's principle. Finally, Navier's solution method is used and the numerical results concerning three different types of shell structures are presented.

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

“…Therefore, there are many studies on FGM plates during the past decades, for example, Refs. [1][2][3][4][5][6][7][8][9][10], to list but only a few. Studies on FGM plates involve many interesting topics, including static and dynamic analyses, stability analysis, buckling analysis, and so on.…”

Mechanical Stability of Hybrid Corrugated Sandwich Plates under Fluid-Structure-Thermal Coupling for Novel Thermal Protection Systems

“…Equivalent single theories and layerwise theories are two approaches that are mostly adopted to model the displacement fields for multi-layered laminated and sandwich plates. Compared to the most commonly used equivalent single theories [32][33][34], such as classic laminate theory, first-order or higher-order shear deformation theory, layerwise theories are capable of predicting more accurate static and dynamic behavior of soft-core sandwich structures by a separate description of displacement fields for each layer [35][36][37][38].…”

A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method

“…Tornabene and Viola [5] studied the dynamical behavior of hemispherical domes and spherical shell panels on the basis of first-order shear deformation theory (FSDT) and generalized differential quadrature (GDQ) method. Jouneghani et al [6] investigated vibrational behavior of doubly curved shells on the basis of first-order shear deformation theory (FSDT) considering porosities. Hamilton's principle and Navier's solution method were both utilized to derive the numerical results.…”