This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate ...This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.展开更多
Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. ...Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. Firstly the mechanical model to analysis the stability of cave roof under pile tip is founded aiming to solve the problems that the simplified mechanical model has. Secondly, the boundary of cave roof is simply supposed to be supported according to the integrity of the rock mass in the boundary of cave roof. Thirdly, based on the theory of plates and shells, the simplified model is calculated and the theoretical calculation formula to determine the safe thickness of cave roof under pile tip can be obtained when the edges of the cave roof are simply supported. In the end, the analysis of the practical engineering project proves the feasibility and the rationality of the method which can be a new method to calculate the safe thickness of cave roof under pile tip.展开更多
A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displaceme...A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and fiexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.展开更多
基金This research is funded by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant number 107.02-2019.330.
文摘This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.
基金Project(14JJ4003) supported by the Natural Science Foundation of Hunan Province,ChinaProject(2013M531812) supported by China Postdoctoral Science Foundation+1 种基金Project supported by the Postdoctoral Foundation of Central South UniversityProject(14JJ4003) Project(2013SCEEKL001) supported by Foundation of Tianjin Key Laboratory of Soft Soil Characteristics and Engineering Environment,China
文摘Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. Firstly the mechanical model to analysis the stability of cave roof under pile tip is founded aiming to solve the problems that the simplified mechanical model has. Secondly, the boundary of cave roof is simply supposed to be supported according to the integrity of the rock mass in the boundary of cave roof. Thirdly, based on the theory of plates and shells, the simplified model is calculated and the theoretical calculation formula to determine the safe thickness of cave roof under pile tip can be obtained when the edges of the cave roof are simply supported. In the end, the analysis of the practical engineering project proves the feasibility and the rationality of the method which can be a new method to calculate the safe thickness of cave roof under pile tip.
基金Foundation item： Project（50975191） supported by the National Natural Science Foundation of China Project（20113027） supported by the Outstanding Innovation Project of Shanxi Province Foundation for Graduate Student
文摘A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and fiexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.
