Vibration analysis of multiple-stepped functionally graded beams with general boundary conditions

2018 ◽  
Vol 186 ◽  
pp. 315-323 ◽  
Author(s):  
Zhu Su ◽  
Guoyong Jin ◽  
Tiangui Ye
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions

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.

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