The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is a...The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.展开更多
Dam structures are prime targets during wars,and a tragedy is likely to happen in a populated area downstream of a dam exposed to explosions.However,experimental investigations of the failure of a concrete gravity dam...Dam structures are prime targets during wars,and a tragedy is likely to happen in a populated area downstream of a dam exposed to explosions.However,experimental investigations of the failure of a concrete gravity dam subjected to underwater explosion(UNDEX)are extremely scarce.In this study,centrifuge tests and numerical simulations were performed to investigate the failure of a concrete gravity dam subjected to a near-field UNDEX.The results revealed the existence of two tensile fractures inside the dam,one in the upper part and the other in the lower part.Due to the narrowness of the upper part,there were coupled effects of bending tensile loads in the upstream face and a reflected tensile stress wave in the downstream face,resulting in severe tensile damage to the upper part in both the upstream and downstream faces.The fracture in the lower part was measured at around one third of the height of the dam.This fracture was produced mainly by the bending tensile loads in the upstream face.Driven by those loads,this fracture started from the upstream face and developed towards the downstream face,with a horizontal angle of about 15?.The underlying mechanisms behind the two tensile fractures were confirmed by recorded strain histories.The dam failures presented in this study are similar to those produced in historical wars,in which dams were under similar attack scenarios.展开更多
In this paper, we study evolution of the universe in the background of f(R, T) gravity using LRS Bianchi type-Ⅰ model. We discuss scale factors as well as deceleration parameter in dark energy dominated era for diffe...In this paper, we study evolution of the universe in the background of f(R, T) gravity using LRS Bianchi type-Ⅰ model. We discuss scale factors as well as deceleration parameter in dark energy dominated era for different bulk viscosity models. The occurrence of big-rip singularity is also examined. It is concluded that expansion is faster when bulk viscosity is proportional to Hubble parameter as compared to other models.展开更多
基金Partially Supported by a Research from Department of Science and Technology(DST),India under Grant No.SB/FTP/MS-003/2013
文摘The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.
基金Project supported by the National Natural Science Foundation of China(Nos.51879283 , 51339006)。
文摘Dam structures are prime targets during wars,and a tragedy is likely to happen in a populated area downstream of a dam exposed to explosions.However,experimental investigations of the failure of a concrete gravity dam subjected to underwater explosion(UNDEX)are extremely scarce.In this study,centrifuge tests and numerical simulations were performed to investigate the failure of a concrete gravity dam subjected to a near-field UNDEX.The results revealed the existence of two tensile fractures inside the dam,one in the upper part and the other in the lower part.Due to the narrowness of the upper part,there were coupled effects of bending tensile loads in the upstream face and a reflected tensile stress wave in the downstream face,resulting in severe tensile damage to the upper part in both the upstream and downstream faces.The fracture in the lower part was measured at around one third of the height of the dam.This fracture was produced mainly by the bending tensile loads in the upstream face.Driven by those loads,this fracture started from the upstream face and developed towards the downstream face,with a horizontal angle of about 15?.The underlying mechanisms behind the two tensile fractures were confirmed by recorded strain histories.The dam failures presented in this study are similar to those produced in historical wars,in which dams were under similar attack scenarios.
基金the Higher Education Commission, Islamabad, Pakistan for its financial support through the Indigenous Ph.D. 5000 Fellowship Program Phase-Ⅱ, Batch-Ⅲ
文摘In this paper, we study evolution of the universe in the background of f(R, T) gravity using LRS Bianchi type-Ⅰ model. We discuss scale factors as well as deceleration parameter in dark energy dominated era for different bulk viscosity models. The occurrence of big-rip singularity is also examined. It is concluded that expansion is faster when bulk viscosity is proportional to Hubble parameter as compared to other models.
