Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates
An analytical solution is presented for axisymmetric free vibration analysis of a functionally graded piezoelectric circular plate on the basis of the three-dimensional elastic theory of piezoelectric materials. The material properties are assumed to follow an exponential law distribution through th...
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2024-12-01
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| author | Yang Li Yang Gao |
| author_facet | Yang Li Yang Gao |
| author_sort | Yang Li |
| collection | DOAJ |
| description | An analytical solution is presented for axisymmetric free vibration analysis of a functionally graded piezoelectric circular plate on the basis of the three-dimensional elastic theory of piezoelectric materials. The material properties are assumed to follow an exponential law distribution through the thickness of the circular plate. The state space equations for the free vibration behavior of the functionally graded piezoelectric circular plate are developed based on the state space method. The finite Hankel transform is utilized to obtain an ordinary differential equation with variable coefficients. By virtue of the proposed exponential law model, we have ordinary differential equations with constant coefficients. Then, the free vibration behaviors of the functionally graded piezoelectric circular plate with two kinds of boundary conditions are investigated. Some numerical examples are given to validate the accuracy and stability of the present model. The influences of the exponential factor and thickness-to-span ratio on the natural frequency of the functionally graded piezoelectric circular plate, constrained by different boundary conditions, are discussed in detail. |
| format | Article |
| id | doaj-art-eec9ece0009647e1a2f328dbf91d3b44 |
| institution | DOAJ |
| issn | 2073-4352 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Crystals |
| spelling | doaj-art-eec9ece0009647e1a2f328dbf91d3b442025-08-20T02:55:32ZengMDPI AGCrystals2073-43522024-12-011412110310.3390/cryst14121103Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular PlatesYang Li0Yang Gao1Department of Aerospace Science and Technology, Space Engineering University, Beijing 101416, ChinaCollege of Science, China Agricultural University, Beijing 100083, ChinaAn analytical solution is presented for axisymmetric free vibration analysis of a functionally graded piezoelectric circular plate on the basis of the three-dimensional elastic theory of piezoelectric materials. The material properties are assumed to follow an exponential law distribution through the thickness of the circular plate. The state space equations for the free vibration behavior of the functionally graded piezoelectric circular plate are developed based on the state space method. The finite Hankel transform is utilized to obtain an ordinary differential equation with variable coefficients. By virtue of the proposed exponential law model, we have ordinary differential equations with constant coefficients. Then, the free vibration behaviors of the functionally graded piezoelectric circular plate with two kinds of boundary conditions are investigated. Some numerical examples are given to validate the accuracy and stability of the present model. The influences of the exponential factor and thickness-to-span ratio on the natural frequency of the functionally graded piezoelectric circular plate, constrained by different boundary conditions, are discussed in detail.https://www.mdpi.com/2073-4352/14/12/1103axisymmetric free vibrationfunctionally graded piezoelectric materialscircular platestate space method |
| spellingShingle | Yang Li Yang Gao Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates Crystals axisymmetric free vibration functionally graded piezoelectric materials circular plate state space method |
| title | Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates |
| title_full | Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates |
| title_fullStr | Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates |
| title_full_unstemmed | Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates |
| title_short | Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates |
| title_sort | axisymmetric free vibration of functionally graded piezoelectric circular plates |
| topic | axisymmetric free vibration functionally graded piezoelectric materials circular plate state space method |
| url | https://www.mdpi.com/2073-4352/14/12/1103 |
| work_keys_str_mv | AT yangli axisymmetricfreevibrationoffunctionallygradedpiezoelectriccircularplates AT yanggao axisymmetricfreevibrationoffunctionallygradedpiezoelectriccircularplates |