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991.
992.
Based on elasticity theory, various two-dimensional (2D) equations and solutions for extensional deformation have been deduced
systematically and directly from the three-dimensional (3D) theory of thick rectangular plates by using the Papkovich–Neuber
solution and the Lur’e method without ad hoc assumptions. These equations and solutions can be used to construct a refined
theory of thick plates for extensional deformation. It is shown that the displacements and stresses of the plate can be represented
by the displacements and transverse normal strain of the midplane. In the case of homogeneous boundary conditions, the exact
solutions for the plate are derived, and the exact equations consist of three governing differential equations: the biharmonic
equation, the shear equation, and the transcendental equation. With the present theory a solution of these can satisfy all
the fundamental equations of 3D elasticity. Moreover, the refined theory of thick plate for bending deformation constructed
by Cheng is improved, and some physical or mathematical explanations and proof are provided to support our justification.
It is important to note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of nonhomogeneous
boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order
terms with respect to plate thickness. The correctness of the stress assumptions in the classic plane-stress problems is revised.
In an example it is shown that the exact or accurate solutions may be obtained by applying the refined theory deduced herein. 相似文献
993.
We have experimentally and analytically studied transport of a passive scalar in the wake of a thin flat plate located at
the centerline of a planar contraction with flat walls. The constant Launder parameter in the contraction, K = 6.25 ×10 − 6, was twice the value required for a turbulent boundary layer to relaminarize. In addition to the mixing analysis inside the
contraction, layer mixing is also investigated downstream, where the flow continues inside a constant cross-section channel.
In order to generate the passive scalar, the airflow above the plate was heated and the temperature stratification in the
wake was traced by measuring the temperature field using constant current anemometry. Using different plate lengths, we found
that the degree of mixing, obtained at a given position in the straight channel, is a function of the distance from the plate
trailing edge to the contraction outlet. For a plate which does not protrude into the straight channel, we demonstrate the
existence of an optimal trailing edge-contraction outlet distance that results in the lowest possible degree of mixing at
a given downstream position in the straight channel. This finding is also supported by a semi-empirical relationship based
on our developed self-similar solution for mixing layers in planar contractions. 相似文献
994.
A novel diffractive optical element, named phase zone photon sieve
(PZPS), is presented. There are three kinds of phase plates in
PZPSs: PZPS1, PZPS2, and PZPS3. Each of the PZPSs has its own
structure and is made on quartz substrate by etching. The three
PZPSs have stronger diffraction peak intensity than a photon sieve
(PS) when the margin pinhole and zone line width are kept the same.
The PZPS3 can produce a smaller central diffractive spot than the
ordinary PS with the same number of zones on the Fresnel zone plate.
We have given the design method for and the simulation of PZPS and
PS. PZPS has potential applications in optical maskless lithography. 相似文献
995.
The symplectic eigenfunction expansion theorem and its application to the plate bending equation 下载免费PDF全文
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner. 相似文献
996.
This paper studies initial-boundary value problems for a class
of nonlinear thermoelastic plate equations. Under some certain
initial data and boundary conditions, it obtains an existence and
uniqueness theorem of global weak solutions of the nonlinear
thermoelstic plate equations, by means of the Galerkin method.
Moreover, it also proves the existence of strong and
classical solutions. 相似文献
997.
根据压电材料修正后的Hellinger-Reissner(H-R)变分原理,建立了各向异性压电材料4节点Hamilton等参元的一般形式.为智能叠层板自由振动问题和带有压电块的叠层悬臂梁的瞬态响应等问题提出了一种新的半解析法.数学模型的基本步骤:将压电层和主体层看成独立的三维体,在平面内离散各层,分别建立各层的方程;根据主体层和压电层在连接界面上广义应力和广义位移的连续条件,联立主体层和压电层的方程得到全结构的控制方程.等参元不限制智能板侧面的几何边界形状、板的厚度和层数,有广泛的应用领域. 相似文献
998.
带弹性附件充液矩形贮箱俯仰运动动态响应 总被引:2,自引:1,他引:1
首先建立了俯仰运动矩形贮箱刚-液-弹耦合系统在外力矩作用下的耦合动力学模型,给出满足边界条件的速度势函数和液面波高的级数表达式,采用伽辽金法离散,将动力学模型转化为常微分方程组,得到刚-液-弹耦合系统的固有频率,给出简单的近似表达式,分析了转动中心距静液面不同位置时刚-液-弹耦合系统各阶固有频率的变化规律,系统转动中心距静液面较近时,耦合后液体反对称模态和刚体的固有频率对比耦合前减小,较远时则增大,最后进行数值验证,比较分析了液体和弹性体对刚体姿态的影响. 相似文献
999.
The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively.Making use of mechan- ical analysis method,by acting couples along the interior edges with suitable evaluations, the deflection surface is divided into piecewise form,therefore,the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate is established.In addition,the interpretation of smoothing cofactor and conformality con- dition from the mechanical point of view is given.Furthermore,by introducing twisting moments,the mechanical background of any spline belong to the above space is set up. 相似文献
1000.
Based on dynamical theories of water waves and dynamics of Mindlin thick plates,the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate are presented using the Wiener-Hopf technique.Without regard to the case of elastic connector,the calculated results obtained by the present method are in good agreement with those from the literature and the experiment.It can be shown that the present method is valid.Relations between the spring stiffness to be used to connect the sea bottom and the floating plate and the parameters of wave-induced responses of floating plates are investigated using the present method.Therefore, these results can be used as theoretical bases for the design stage of super floating platform systems. 相似文献