Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions
This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on a...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2017/3425298 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832546516678475776 |
|---|---|
| author | Huimin Liu Fanming Liu Xin Jing Zhenpeng Wang Linlin Xia |
| author_facet | Huimin Liu Fanming Liu Xin Jing Zhenpeng Wang Linlin Xia |
| author_sort | Huimin Liu |
| collection | DOAJ |
| description | This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique. |
| format | Article |
| id | doaj-art-2fc52363062e4be2a9a4bf4deab5d218 |
| 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-2fc52363062e4be2a9a4bf4deab5d2182025-02-03T06:48:28ZengWileyShock and Vibration1070-96221875-92032017-01-01201710.1155/2017/34252983425298Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary ConditionsHuimin Liu0Fanming Liu1Xin Jing2Zhenpeng Wang3Linlin Xia4College of Automation, Harbin Engineering University, Harbin, ChinaCollege of Automation, Harbin Engineering University, Harbin, ChinaCollege of Automation, Harbin Engineering University, Harbin, ChinaCollege of Automation, Harbin Engineering University, Harbin, ChinaSchool of Automation Engineering, Northeast Dianli University, Jilin, ChinaThis paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.http://dx.doi.org/10.1155/2017/3425298 |
| spellingShingle | Huimin Liu Fanming Liu Xin Jing Zhenpeng Wang Linlin Xia Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions Shock and Vibration |
| title | Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions |
| title_full | Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions |
| title_fullStr | Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions |
| title_full_unstemmed | Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions |
| title_short | Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions |
| title_sort | three dimensional vibration analysis of rectangular thick plates on pasternak foundation with arbitrary boundary conditions |
| url | http://dx.doi.org/10.1155/2017/3425298 |
| work_keys_str_mv | AT huiminliu threedimensionalvibrationanalysisofrectangularthickplatesonpasternakfoundationwitharbitraryboundaryconditions AT fanmingliu threedimensionalvibrationanalysisofrectangularthickplatesonpasternakfoundationwitharbitraryboundaryconditions AT xinjing threedimensionalvibrationanalysisofrectangularthickplatesonpasternakfoundationwitharbitraryboundaryconditions AT zhenpengwang threedimensionalvibrationanalysisofrectangularthickplatesonpasternakfoundationwitharbitraryboundaryconditions AT linlinxia threedimensionalvibrationanalysisofrectangularthickplatesonpasternakfoundationwitharbitraryboundaryconditions |