The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD third-grade fl...The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD third-grade fluid in presence of Hall currents. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformations. The complex analytical solution is found by using the homotopy analysis method (HAM). The existing literature on the topic shows that it is the first study regarding the effects of Hall current on flow of an unsteady MHD third-grade fluid over an impulsively moving plane wall. The convergence of the obtained complex series solutions is carefully analyzed. The effects of dimensionless parameters on the velocity are illustrated through plots and the effects of the pertinent parameters on the local skin friction coefficient at the surface of the wall are presented numerically in tabular form.展开更多
Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs...Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.展开更多
In this pap er, a novel size-dep endent functionally graded (FG) cylindrical shell model is develop ed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory . Th...In this pap er, a novel size-dep endent functionally graded (FG) cylindrical shell model is develop ed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory . The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical typ es of size e ects simultaneously , which are the nonlocal stress ef- fect, the strain gradient e ect, and the surface energy e ects. With the help of Hamilton’s principle and rst-order shear deformation theory , the non-classical governing equations and related b oundary conditions are derived. By using the prop osed model, the free vibra- tion problem of FG cylindrical nanoshells with material prop erties varying continuously through the thickness according to a p ower-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various b oundary conditions are obtained. After verifying the reliability of the prop osed model and analytical method by comparing the degenerated results with those available in the literature, the in uences of nonlocal parameter, material length scale parameter, p ower-law index, radius-to-thickness ratio, length-to-radius ratio, and surface e ects on the vibration characteristic of func- tionally graded cylindrical nanoshells are examined in detail.展开更多
该研究的目的是将能量辐射传递法(radiative energy transfer method,RETM)推广到功能梯度板模型中,以预测结构的高频振动响应。基于一阶剪切变形理论推导了功能梯度板的振动控制方程,获得了波传播特性参数。在该方法中,结构内部的能量...该研究的目的是将能量辐射传递法(radiative energy transfer method,RETM)推广到功能梯度板模型中,以预测结构的高频振动响应。基于一阶剪切变形理论推导了功能梯度板的振动控制方程,获得了波传播特性参数。在该方法中,结构内部的能量响应由激励产生的直接场与边界虚源产生的反射场叠加得到。在临界频率以下,能量响应由一种传播波控制;而在临界频率以上,由三种传播波控制。数值算例结果与模态叠加法和功率流分析进行了对比,验证了RETM在计算不同物理参数下功能梯度板高频振动响应的准确性。研究了不同厚度下剪切变形和转动惯量对能量响应的影响,讨论了材料梯度因子、结构阻尼和激励频率对高频振动能量的影响。结果表明,材料梯度因子的变化会导致结构波传播特性和能量分布特征的变化,越大能量的衰减速度越快,衰减幅度越大。展开更多
文摘The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD third-grade fluid in presence of Hall currents. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformations. The complex analytical solution is found by using the homotopy analysis method (HAM). The existing literature on the topic shows that it is the first study regarding the effects of Hall current on flow of an unsteady MHD third-grade fluid over an impulsively moving plane wall. The convergence of the obtained complex series solutions is carefully analyzed. The effects of dimensionless parameters on the velocity are illustrated through plots and the effects of the pertinent parameters on the local skin friction coefficient at the surface of the wall are presented numerically in tabular form.
文摘Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.
基金Project supported by the National Natural Science Foundation of China(Nos.11872233 and11472163)the China Scholarship Council(No.201706890041)the Innovation Program of Shanghai Municipal Education Commission(No.2017-01-07-00-09-E00019)
文摘In this pap er, a novel size-dep endent functionally graded (FG) cylindrical shell model is develop ed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory . The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical typ es of size e ects simultaneously , which are the nonlocal stress ef- fect, the strain gradient e ect, and the surface energy e ects. With the help of Hamilton’s principle and rst-order shear deformation theory , the non-classical governing equations and related b oundary conditions are derived. By using the prop osed model, the free vibra- tion problem of FG cylindrical nanoshells with material prop erties varying continuously through the thickness according to a p ower-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various b oundary conditions are obtained. After verifying the reliability of the prop osed model and analytical method by comparing the degenerated results with those available in the literature, the in uences of nonlocal parameter, material length scale parameter, p ower-law index, radius-to-thickness ratio, length-to-radius ratio, and surface e ects on the vibration characteristic of func- tionally graded cylindrical nanoshells are examined in detail.
文摘该研究的目的是将能量辐射传递法(radiative energy transfer method,RETM)推广到功能梯度板模型中,以预测结构的高频振动响应。基于一阶剪切变形理论推导了功能梯度板的振动控制方程,获得了波传播特性参数。在该方法中,结构内部的能量响应由激励产生的直接场与边界虚源产生的反射场叠加得到。在临界频率以下,能量响应由一种传播波控制;而在临界频率以上,由三种传播波控制。数值算例结果与模态叠加法和功率流分析进行了对比,验证了RETM在计算不同物理参数下功能梯度板高频振动响应的准确性。研究了不同厚度下剪切变形和转动惯量对能量响应的影响,讨论了材料梯度因子、结构阻尼和激励频率对高频振动能量的影响。结果表明,材料梯度因子的变化会导致结构波传播特性和能量分布特征的变化,越大能量的衰减速度越快,衰减幅度越大。
