A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions

Su, Zhu; Jin, Guoyong; Shi, Shuangxia; Ye, Tiangui; Jia, Xingzhao

doi:10.1016/j.ijmecsci.2014.01.002

Cited by 144 publications

(27 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Aragh and Hedayati [6] dealt with the free vibration and static response of a twodimensional functionally graded (2D FGM) metal/ceramic open cylindrical shell with classical boundary conditions by using 2D generalized differential quadrature method. Su et al [7][8][9] applied the modified Fourier series and Rayleigh-Ritz method to analyze the free vibrations of functionally graded open and closed shells including cylindrical, conical, and spherical ones with general boundary conditions based on first-order shear deformation theory. Sofiyev and Kuruoglu [10][11][12][13] presented a theoretical approach on the basis of the Galerkin method to solve vibration problems of functionally graded (FG) truncated and complete conical shells under mixed classical boundary conditions and resting on elastic 2 Mathematical Problems in Engineering foundations.…”

Section: Introductionmentioning

confidence: 99%

“…However, from the literatures review, we also know that the most existing numerical solutions for the title problem usually take account of a onefold computational model instead of unified computational model. For instance, Su et al [7][8][9] divided the open and closed functionally graded cylindrical, conical, spherical shells to study and resort different admissible functions by means of the modified Fourier series technology. However, in practical project application, the structural forms are generally unknown.…”

Section: Introductionmentioning

confidence: 99%

“…In order to check the present method, the numerical results reported by Su et al [7][8][9], Qu et al [27], and Tornabene et al [1,3,52] are also given in the above tables for comparison. From the comparisons, we can see a consistent agreement of present results taken from the current proposed unified approach and referential data.…”

mentioning

confidence: 99%

See 2 more Smart Citations

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Pang

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Pang

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Alijani et al [31] investigated the nonlinear forced vibrations of simply supported FG doubly curved shallow shells based on Donnell's nonlinear shallow shell theory and the Galerkin method. Su et al [32] presented a unified solution for vibration analysis of FG cylindrical, conical shells and annular plates with general boundary conditions by applying the FSDT and Rayleigh-Ritz procedure. Qu et al [33] described a unified formulation for free, steady-state, and transient vibration analyses of FG shells with arbitrary boundary conditions on the basis of the FSDT.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Shi

Zha

Zhang

et al. 2017

Shock and Vibration

View full text Add to dashboard Cite

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and RayleighRitz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

show abstract

“…Later, the method fast extended to cope with other structures (i.e. beams, plates, shells and coupled structures) by the Du [27][28][29][30], Jin [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], Wang et al [47][48][49][50][51][52] in the last ten years due to the superiority compared with other methods. The detailed theoretical analyses and mathematical principle can been seen in Refs [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

Wang

Shi

Pang

et al. 2016

Curved and Layered Structures

View full text Add to dashboard Cite

A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.

show abstract

A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions

Cited by 144 publications

References 48 publications

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

Contact Info

Product

Resources

About