Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory
This paper studies the free vibration characteristics of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory (SFSDT), which contains only four unknown displacement components. The arbitrary straight-sided quadrilateral plate is mapped into a unit square...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-12-01
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| Series: | Results in Physics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379718315468 |
| _version_ | 1819163584696942592 |
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| author | Dongyan Shi Tao Liu Qingshan Wang Qi Lan |
| author_facet | Dongyan Shi Tao Liu Qingshan Wang Qi Lan |
| author_sort | Dongyan Shi |
| collection | DOAJ |
| description | This paper studies the free vibration characteristics of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory (SFSDT), which contains only four unknown displacement components. The arbitrary straight-sided quadrilateral plate is mapped into a unit square plate uniformly, and accordingly, the problem can be solved directly by the existing vibration modeling method of rectangular plate. The admissible functions of displacements are generally expressed as superposition of the periodic functions based on the improved Fourier series method. All the series expansion coefficients can be determined by the Rayleigh-Ritz procedure. Combined with the artificial virtual spring technology, the present method could be used to analyze the vibration characteristics of quadrilateral plates under arbitrary boundary conditions. Convergence and accuracy of the present method are checked out through some numerical examples of plate with rectangular, skew, trapezoidal and general quadrilateral shapes, and various boundary conditions. In addition, some new results and new conclusions have been given as the benchmark for future research. Keywords: Simple first-order shear deformation theory, Quadrilateral plate, Arbitrary shapes, Improved Fourier series method, Arbitrary boundary conditions, Rayleigh-Ritz technique |
| first_indexed | 2024-12-22T17:46:28Z |
| format | Article |
| id | doaj.art-f448a08f80fd4ecfaf8039e1ed8efe64 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-22T17:46:28Z |
| publishDate | 2018-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-f448a08f80fd4ecfaf8039e1ed8efe642022-12-21T18:18:17ZengElsevierResults in Physics2211-37972018-12-0111201211Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theoryDongyan Shi0Tao Liu1Qingshan Wang2Qi Lan3College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, PR ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, PR ChinaState Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, PR China; Corresponding author.Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UKThis paper studies the free vibration characteristics of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory (SFSDT), which contains only four unknown displacement components. The arbitrary straight-sided quadrilateral plate is mapped into a unit square plate uniformly, and accordingly, the problem can be solved directly by the existing vibration modeling method of rectangular plate. The admissible functions of displacements are generally expressed as superposition of the periodic functions based on the improved Fourier series method. All the series expansion coefficients can be determined by the Rayleigh-Ritz procedure. Combined with the artificial virtual spring technology, the present method could be used to analyze the vibration characteristics of quadrilateral plates under arbitrary boundary conditions. Convergence and accuracy of the present method are checked out through some numerical examples of plate with rectangular, skew, trapezoidal and general quadrilateral shapes, and various boundary conditions. In addition, some new results and new conclusions have been given as the benchmark for future research. Keywords: Simple first-order shear deformation theory, Quadrilateral plate, Arbitrary shapes, Improved Fourier series method, Arbitrary boundary conditions, Rayleigh-Ritz techniquehttp://www.sciencedirect.com/science/article/pii/S2211379718315468 |
| spellingShingle | Dongyan Shi Tao Liu Qingshan Wang Qi Lan Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory Results in Physics |
| title | Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory |
| title_full | Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory |
| title_fullStr | Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory |
| title_full_unstemmed | Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory |
| title_short | Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory |
| title_sort | vibration analysis of arbitrary straight sided quadrilateral plates using a simple first order shear deformation theory |
| url | http://www.sciencedirect.com/science/article/pii/S2211379718315468 |
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