Sound transmission analysis of functionally graded material plates with general boundary conditions in thermal environments

2021 ◽  
Vol 174 ◽  
pp. 107795
Author(s):  
Zhengmin Hu ◽  
Kai Zhou ◽  
Shizhang Huang ◽  
Yong Chen
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Sound Transmission ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Thermal Environments ◽  
Graded Material

Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions

2018 ◽  
Vol 233 (8) ◽  
pp. 2636-2662 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Mohammad Sikandar Azam ◽  
Vinayak Ranjan
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Functionally Graded Plate ◽  
Material Inhomogeneity ◽  
Power Law Exponent ◽  
Out Of Plane ◽  
Graded Material

In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequency parameters (nondimensional natural frequencies) has been attained by increasing the number of polynomials of displacement function. The frequency parameters of the functionally graded material plate obtained by proposed method are compared with the open literature to validate the present model. Firstly, the present model is used to calculate first six natural frequencies of the functionally graded plate under all possible combinations of boundary conditions for the constant value of stiffness of Winkler and Pasternak foundation moduli. Further, the effects of density, aspect ratio, power law exponent, Young’s modulus on frequency parameters of the functionally graded plate resting on Winkler–Pasternak foundation under specific boundary conditions viz. CCCC (all edges clamped), SSSS (all edges simply supported), CFFF (cantilever), SCSF (simply supported-clamped-free) are studied extensively. Furthermore, effect of stiffness of elastic foundation moduli (kp and kw) on frequency parameters are analyzed. It has been observed that effects of aspect ratios, boundary conditions, Young’s modulus and density on frequency parameters are significant at lower value of the power law exponent. It has also been noted from present investigation that Pasternak foundation modulus has greater effect on frequency parameters as compared to the Winkler foundation modulus. Most of the results presented in this paper are novel and may be used for the validation purpose by researchers. Three dimensional mode shapes for the functionally graded plate resting on elastic foundation have also been presented in this article.

A Unified Modeling Method for Dynamic Analyses of FGP Annular and Circular Plates with General Boundary Conditions

2021 ◽  
Author(s):  
J. Lu ◽  
X. Hua ◽  
C. Chiu ◽  
X. Zhang ◽  
S. Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Modeling Method ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Circular Plates ◽  
Unified Modeling ◽  
Dynamic Analyses ◽  
Vibration Responses

The porous material is an emerging lightweight material, which is able to reduce structural weight and also keeps the superiority of the structure. Therefore, this work is devoted to the investigation of the functionally graded porous (FGP) annular and circular plates with general boundary conditions. The unified modeling method is proposed by combining the first-order shear deformation theory, the virtual spring technology, the multi-segment partition method, and the semi-analysis Rayleigh–Ritz approach. Afterwards, the convergency and correctness of the proposed method are verified, respectively. The frequency parameters, modal shapes, and forced vibration responses are uniformly calculated based on the proposed method. Finally, the dynamic analyses of the FGP annular and circular plates with different parameters, such as the porosity distribution types, porosity ratios, boundary condition types, geometry parameters, and load types, are conducted in detail. It is found that the reasonable porous design is able to keep the dynamic stability of the structure under different parameter variations.

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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