Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with 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, accor...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2017/7025190 |
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| _version_ | 1832552500792655872 |
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| author | Dongyan Shi Shuai Zha Hong Zhang Qingshan Wang |
| author_facet | Dongyan Shi Shuai Zha Hong Zhang Qingshan Wang |
| author_sort | Dongyan Shi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-58124c9e891a490d8bc294e0c5c5b3b0 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-58124c9e891a490d8bc294e0c5c5b3b02025-02-03T05:58:28ZengWileyShock and Vibration1070-96221875-92032017-01-01201710.1155/2017/70251907025190Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary ConditionsDongyan Shi0Shuai Zha1Hong Zhang2Qingshan Wang3College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaThe 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.http://dx.doi.org/10.1155/2017/7025190 |
| spellingShingle | Dongyan Shi Shuai Zha Hong Zhang Qingshan Wang Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions Shock and Vibration |
| title | Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions |
| title_full | Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions |
| title_fullStr | Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions |
| title_full_unstemmed | Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions |
| title_short | Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions |
| title_sort | free vibration analysis of the unified functionally graded shallow shell with general boundary conditions |
| url | http://dx.doi.org/10.1155/2017/7025190 |
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