Free vibration analysis of functionally graded porous cylindrical panels and shells with porosity distributions along the thickness and length directions

Abstract

This paper mainly investigates the free vibration behaviors of functionally graded porous (FGP) cylindrical panels and shells. According to the direction and type of porosity distribution, besides three typical thickness-direction distribution kinds: symmetric, non-symmetric and uniform, two new distribution types along the length direction: symmetric and non-symmetric are considered for the first time. By utilizing the first order shear deformation theory (FSDT) in conjunction with Hamilton’s principle, the weak form for free vibration of FGP shells is derived. Then the isogeometric analysis (IGA) method is applied to solve this problem, in which the non-uniform rational B-spline (NURBS) is employed to both exactly build geometric model and approximately describe displacement fields. The accuracy of IGA-FSDT is examined via comparing the current results with published data. Several numerical examples for FGP cylindrical panels and shells are presented and discussed in terms of porosity coefficient, boundary conditions, geometric parameters and types of porosity distributions. Some innovative results may provide benchmark solutions for other algorithm research and some guidelines for designing FGP structures.