A comparison of FEM and DIQM in investigating the nonlinear free vibration of axially functionally graded tapered microbeams with general boundary conditions

2021 ◽  
pp. 115027
Author(s):  
S.A. Mohamed ◽  
Laila Gamal ◽  
Rabab A. Shanab ◽  
Atef Eraky Bakry
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Nonlinear Free Vibration

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

2017 ◽  
Vol 4 (1) ◽  
pp. 52-84 ◽  
Author(s):  
Hong Zhang ◽  
Dongyan Shi ◽  
Qingshan Wang ◽  
Bin Qin
Keyword(s):  
Fourier Series ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Power Law ◽  
Admissible Function ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Series Method ◽  
Fourier Series Method

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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