In this paper, the free vibrations of functionally graded porous (FGP) rectangular plate with uniform elastic boundary conditions is investigated by means of an improved Fourier series method (IFSM). It is assumed that the distributions of porosity are uniform or non-uniformly along a certain direction and three types of the porosity distribution are considered, among which material property of two non-uniform porous distributions was expressed as the simple cosine. The size of the pore in a rectangular plate is determined by the porosity coefficients. Using the first-order shear deformation theory(FSDT), the energy expression of FGP rectangular plate is created. In order to obtain the admissible function of displacement for functionally graded porous rectangular plate, the IFSM is employed. Then, the Rayleigh-Ritz method is used to solve coefficients in the Fourier series which determine natural frequencies and modal shapes. Convergence and comparative research are performed to prove the convergence, reliability and accuracy of the current method. On this foundation, some new results covering the influence of the geometrical parameters subject to classical and elastic boundary condition are presented, and the parametric studies are also investigated in detail, which can provide a reference for future research by other researchers.

Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions

As a novel class of weight-efficient engineering materials, the functionally graded porous (FGP) beam structures have great potential value. However, the current research on it is relatively small. Based on this research status, the aim of this paper is establishing a unified analytical model to study the vibration behavior of moderately thick functionally graded porous deep curved and straight beam with general boundary conditions. The first-order beam theory which considering the influence of shear deformation, inertia rotary and deepness term are adopted in the formulation. The theoretical solution model is obtained by means of modified series solution which core soul is using the modified Fourier series including a standard cosine Fourier series with two auxiliary terms to expand the admissible function. This fact gives the opportunity to derive the exact solution for FGP beam with general boundary conditions by utilizing a reasonable spring stiffness value at both ends. A series of numerical examples show that the current model has superior convergence characteristics, computational accuracy and stability. On this basis, a series of innovative results are also highlighted in the text, which may be providing basic data for other algorithm research in the future.

A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams

In this research, an analytical Jacobi-Ritz method for the free vibration analysis of composite laminated rectangular plate subject to arbitrary boundary conditions is proposed. The theoretical model is constructed in the framework of the first-order shear deformation theory (FSDT), and the multi-segment partitioning strategy is introduced. The boundary condition as well as the interface continuity condition is dealt with through the artificial spring technique. The displacement functions for every separated plate segment are expanded in the way of Jacobi polynomials along both the length and width orientations. And all the undetermined coefficients are decided through the Ritz method. The solution exhibits excellent convergence performance and shows stable features. The reliability and precision of the proposed methodology are validated by comparison with results from literature, where general boundary conditions are taken into account. Furthermore, parameterized study of the composite laminated rectangular plate is conducted, the results of which can be benchmark results for the future study.

A unified formulation for free vibration of laminated plate through Jacobi-Ritz method

This research presents the agglomeration effect of reinforcements on wave propagation analysis of multi-scale hybrid nanocomposite shell based on first-order shear deformable theory (FSDT) of shell...

Wave propagation response of multi-scale hybrid nanocomposite shell by considering aggregation effect of CNTs

A new three-dimensional exact solution for the free vibrations of arbitrary thick functionally graded annular sector plates with arbitrary boundary conditions is presented. The three-dimensional elasticity theory is employed to formulate the theoretical model. According to a power law distribution of the volume of the constituents, the material properties change continuously through the thickness of the functionally graded annular sector plates. Each of displacements of the annular sector plates, regardless of boundary conditions, is expanded as a three-dimensional (3-D) Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities with the displacements and its derivatives at the edges. Since the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on the Ritz procedure by the energy functions of plate. The excellent accuracy and reliability of the current solutions are demonstrated by numerical examples and comparison of the present results with those available in the literature, and numerous new results for thick FG annular sector plates with elastic boundary conditions are presented. The effects of gradient indexes are also illustrated.

Three-dimensional exact solution for the free vibration of thick functionally graded annular sector plates with arbitrary boundary conditions

A modeling method for vibration analysis of cracked laminated composite beam of uniform rectangular cross-section with arbitrary boundary condition

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A modeling method for vibration analysis of cracked laminated composite beam of uniform rectangular cross-section with arbitrary boundary condition