This paper presents an analytical study on the influence of edge restraining stiffness on the transverse vibrations of rectangular plate structure. An improved Fourier series method was employed to analyze the transve...This paper presents an analytical study on the influence of edge restraining stiffness on the transverse vibrations of rectangular plate structure. An improved Fourier series method was employed to analyze the transverse vibration of plate structure with general elastically restrained boundary conditions. A linear combination of a double Fourier series and eight auxiliary terms was sought as the admissible function of the flexural displacement of the plate, each term being a combination of a polynomial function and a single cosine series expansion. The auxiliary terms were introduced to ensure and improve the smoothness of the original displacement function and its derivatives at the boundaries. Several numerical examples were given to demonstrate the validity and accuracy of the current solution. The influences of translational and rotational stiffness on the natural frequencies and mode shapes of plate were analyzed by numerical results. The results show that the translational stiffness has bigger influence on the natural frequencies than the rotational stiffness. It is generally well known that little change of the rotational stiffness has little influence on the mode shapes of plate. However, the current work shows that a very little change of rotational stiffness value may lead to a large change of the mode shapes of a square plate structure.展开更多
This paper presents a general solution for active earth pressure acting on a vertical retaining wall with a drainage system along the soil-structure interface. The backfill has a horizontal surface and is composed of ...This paper presents a general solution for active earth pressure acting on a vertical retaining wall with a drainage system along the soil-structure interface. The backfill has a horizontal surface and is composed of cohesionless and fully saturated sand with anisotropic permeability along the vertical and horizontal directions. The extremely unfavourable seepage flow on the back of the retaining wall due to heavy rainfall or other causes will dramatically increase the active earth pressure acting on the retaining walls, increasing the probability of instability. In this paper, an analytical solution to the Laplace differential governing equation is presented for seepage problems considering anisotropic permeability based on Fourier series expansion method. A good correlation is observed between this and the seepage forces along a planar surface generated via finite element analysis. The active earth pressure is calculated using Coulomb's earth pressure theory based on the calculated pore water pressures. The obtained solutions can be degenerated into Coulomb's formula when no seepage exists in the backfill. A parametric study on the influence of the degree of anisotropy in seepage flow on the distribution of active earth pressure behind the wall is conducted by varying ratios of permeability coefficients in the vertical and horizontal directions,showing that anisotropic seepage flow has a prominent impact on active earth pressure distribution. Other factors such as effective internal friction angle of soils and soil/wall friction conditions are also considered.展开更多
基金the National Natural Science Foundation of China (No.10802024)Research Fund for the Doctoral Program of Higher Education of China (No.200802171009)+2 种基金Natural Science Foundation of Heilongjiang Province (No.E200944)Innovative Talents Fund of Harbin (No.2009RFQXG211)Fundamental Research Fund of HEU (No. HEUFT08003)
文摘This paper presents an analytical study on the influence of edge restraining stiffness on the transverse vibrations of rectangular plate structure. An improved Fourier series method was employed to analyze the transverse vibration of plate structure with general elastically restrained boundary conditions. A linear combination of a double Fourier series and eight auxiliary terms was sought as the admissible function of the flexural displacement of the plate, each term being a combination of a polynomial function and a single cosine series expansion. The auxiliary terms were introduced to ensure and improve the smoothness of the original displacement function and its derivatives at the boundaries. Several numerical examples were given to demonstrate the validity and accuracy of the current solution. The influences of translational and rotational stiffness on the natural frequencies and mode shapes of plate were analyzed by numerical results. The results show that the translational stiffness has bigger influence on the natural frequencies than the rotational stiffness. It is generally well known that little change of the rotational stiffness has little influence on the mode shapes of plate. However, the current work shows that a very little change of rotational stiffness value may lead to a large change of the mode shapes of a square plate structure.
基金supported by the National Key R & D program of China (Grant No. 2016YFC0800204)the National Key Basic Research Program of China (Grant No. 2015CB057801)Natural Science Foundation of China (Grant Nos. 51578499 & 51761130078)
文摘This paper presents a general solution for active earth pressure acting on a vertical retaining wall with a drainage system along the soil-structure interface. The backfill has a horizontal surface and is composed of cohesionless and fully saturated sand with anisotropic permeability along the vertical and horizontal directions. The extremely unfavourable seepage flow on the back of the retaining wall due to heavy rainfall or other causes will dramatically increase the active earth pressure acting on the retaining walls, increasing the probability of instability. In this paper, an analytical solution to the Laplace differential governing equation is presented for seepage problems considering anisotropic permeability based on Fourier series expansion method. A good correlation is observed between this and the seepage forces along a planar surface generated via finite element analysis. The active earth pressure is calculated using Coulomb's earth pressure theory based on the calculated pore water pressures. The obtained solutions can be degenerated into Coulomb's formula when no seepage exists in the backfill. A parametric study on the influence of the degree of anisotropy in seepage flow on the distribution of active earth pressure behind the wall is conducted by varying ratios of permeability coefficients in the vertical and horizontal directions,showing that anisotropic seepage flow has a prominent impact on active earth pressure distribution. Other factors such as effective internal friction angle of soils and soil/wall friction conditions are also considered.
