Free vibration of functionally graded parabolic and circular panels with general boundary conditions

AbstractThe purpose of this content is to investigate the free vibration of functionally graded parabolic and circular panels with general boundary conditions by using the Fourier-Ritz method. The first-order shear deformation theory is adopted to consider the effects of the transverse shear and rotary inertia of the panel structures. The functionally graded panel structures consist of ceramic and metal which are assumed to vary continuously through the thickness according to the power-law distribution, and two types of power-law distributions are considered for the ceramic volume fraction. The improved Fourier series method is applied to construct the new admissible function of the panels to surmount the weakness of the relevant discontinuities with the original displacement and its derivatives at the boundaries while using the traditional Fourier series method. The boundary spring technique is adopted to simulate the general boundary condition. The unknown coefficients appearing in the admissible function are determined by using the Ritz procedure based on the energy functional of the panels. The numerical results show the present method has good convergence, reliability and accuracy. Some new results for functionally graded parabolic and circular panels with different material distributions and boundary conditions are provided, which may serve as benchmark solutions.

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

Engineering Computations ◽

10.1108/ec-06-2016-0218 ◽

2017 ◽

Vol 34 (5) ◽

pp. 1598-1641 ◽

Cited By ~ 8

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.

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Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Shock and Vibration ◽

10.1155/2017/4018629 ◽

2017 ◽

Vol 2017 ◽

pp. 1-35 ◽

Cited By ~ 10

Author(s):

Haichao Li ◽

Fuzhen Pang ◽

Xueren Wang ◽

Shuo Li

Keyword(s):

Fourier Series ◽

Free Vibration ◽

Boundary Conditions ◽

Elastic Foundation ◽

Functionally Graded ◽

General Boundary ◽

General Boundary Conditions ◽

Special Cases ◽

Ritz Procedure ◽

Two Parameter

The free vibration analysis of moderately thick functionally graded (FG) sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the power-law distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT) is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.

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

Shock and Vibration ◽

10.1155/2017/7025190 ◽

2017 ◽

Vol 2017 ◽

pp. 1-19 ◽

Cited By ~ 4

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.

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