Vibration behavior of the functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method

Abstract

The main goal of this article is to provide parameterization study for vibration behavior of functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method. Distribution of the porous through the thickness of structure may be uniform or non-uniform and three types of the porosity distributions are performed in this paper. Mechanical properties of materials are determined by open-cell metal foam. Energy expressions, including kinetic energy and potential energy, are expressed by displacement admissible function. Then, in order to obtain the general boundary conditions including the simply classical boundary conditions, elastic boundary constraint and their combinatorial boundary constraints, each of displacement admissible functions is expanded as a modified Fourier series of a standard cosine Fourier series with the auxiliary functions introduced to eliminate all potential discontinuities of the original displacement function and its derivatives at the edges. Lastly, the natural frequencies as well as the associated mode shapes of FGP doubly-curved panels and shells of revolution are achieved by replacing the modified Fourier series into the above energy expression and using the variational operation for unknown expansion coefficients. The convergence and accuracy of the present modeling are validated by comparing its results with those available in the literature and FEM results. Based on that, a series of innovative results are also highlighted in the text, which may provide basic data for other algorithm research in the future.