scholarly journals Free vibration of four-parameter functionally graded moderately thick doubly-curved panels and shells of revolution with general boundary conditions

2017 ◽  
Vol 42 ◽  
pp. 705-734 ◽  
Author(s):  
Qingshan Wang ◽  
Dongyan Shi ◽  
Qian Liang ◽  
Fuzhen Pang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Shells Of Revolution ◽  
Doubly Curved ◽  
Curved Panels

Free vibration of moderately thick functionally graded parabolic and circular panels and shells of revolution with general boundary conditions

2017 ◽  
Vol 34 (5) ◽  
pp. 1598-1641 ◽  
Author(s):  
Qingshan Wang ◽  
Dongyan Shi ◽  
Qian Liang ◽  
Fuzhen Pang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Power Law ◽  
Ritz Method ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Shells Of Revolution ◽  
Content Type ◽  
Vibration Behavior

Purpose The purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels and shells of revolution with general boundary conditions. Design/methodology/approach The modified Fourier series is chosen as the basis function of the admissible functions of the structure to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges, and the vibration behavior is solved by means of the Ritz method. The complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of FG parabolic and circular panels at the common meridian of θ = 0 and 2π. The convergence and accuracy of the present method are verified by other contributors. Findings Some new results of FG panels and shells with elastic restraints, as well as different geometric and material parameters, are presented and the effects of the elastic restraint parameters, power-law exponent, circumference angle and power-law distributions on the free vibration characteristic of the panels are also presented, which can be served as benchmark data for the designers and engineers to avoid the unpleasant, inefficient and structurally damaging resonant. Originality/value The paper could provide the reference for the research about the moderately thick FG parabolic and circular panels and shells of revolution with general boundary conditions. In addition, the change of the boundary conditions can be easily achieved by just varying the stiffness of the boundary restraining springs along all the edges of panels without making any changes in the solution procedure.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Dongyan Shi ◽  
Shuai Zha ◽  
Hong Zhang ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
General Boundary ◽  
Volume Distribution ◽  
General Boundary Conditions

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 Rayleigh-Ritz 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.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-32 ◽  
Author(s):  
Lijie Li ◽  
Haichao Li ◽  
Fuzhen Pang ◽  
Xueren Wang ◽  
Yuan Du ◽  
...  
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Condition ◽  
Shells Of Revolution ◽  
Fourier Cosine ◽  
Cosine Series

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.

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