共查询到20条相似文献,搜索用时 31 毫秒
1.
The exact solution of Stokes' second problem including start-up process with fractional element 总被引:1,自引:1,他引:0
The start-up process of Stokes' second problem of a viscoelastic material with fractional element is studied. The fluid above an infinite flat plane is set in motion by a sudden acceleration of the plate to steady oscillation. Exact solutions are obtained by using Laplace transform and Fourier transform. It is found that the relationship between the first peak value and the one of equal-amplitude oscillations depends on the distance from the plate. The amplitude decreases for increasing frequency and increasing distance. 相似文献
2.
M. Emin Erdo?an 《International Journal of Non》2009,44(1):27-30
The unsteady flow over a plane wall which is initially at rest and the plate begins suddenly to oscillate in own plane is considered. The solution subject to the boundary and initial conditions is obtained by applying to the governing equation the Laplace transform method or Fourier transform method. A comparison of the solutions obtained by two transform methods for flow considered is given. It is shown that the solution obtained by the Laplace transform method or Fourier transform method is the sum of the steady-state and the transient parts. The transient parts are found in terms of definite integrands whose integrals are oscillatory functions. Therefore, the transient parts are expressed in terms of the tabulated functions. 相似文献
3.
The unsteady motion of an incompressible micropolar fluid filling a half-space bounded by a horizontal infinite plate that started to move suddenly is considered. Laplace transform techniques are used. The solution in the Laplace transform domain is obtained by using a direct approach. The inverse Laplace transforms are obtained in an exact manner using the complex inversion formula of the transform together with contour integration techniques. The solution in the case of classical viscous fluids is recovered as a special case of this work when the micropolarity coecient is assumed to be zero. Numerical computations are carried out and represented graphically. 相似文献
4.
A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite,fluid-loaded plate is presented.The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners,which are assumed to be line forces.The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Green’s function and Fourier transform methods.Using the boundary conditions and space harmonic method,we establish the relationship between the stiffener forces and the vibration displacement of the plate.In this paper,the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement,which are calculated by using a numerical reduction technique.Finally,the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space.Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly. 相似文献
5.
The unsteady Couette flow between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates
in a rotating system under the boundary layer approximations is investigated. An exact solution of the governing equations
has been obtained by using Laplace transform technique. It is shown that when the oscillating plate situated at an infinite
distance from stationary plate then the problem reduces to the unsteady boundary layer problem in a rotating system with non-torsional
oscillations of the free-stream velocity. 相似文献
6.
In this paper, the flow of a visco-elastic liquid between two parallel plates has been studied when one plate is stationary and the other plate suddenly starts oscillating. Both finite Fourier sine transform and Laplace transform technique have been employed to solve the basic differential equations. The flow phenomenon has been characterized by the parameters, and and the effects of these on the flow characteristics have been studied through several graphs.Late professor of the department, who died in an accident on 7th July 1978. 相似文献
7.
The problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an orthotropic elastic plate of constant thickness subjected to out-of-plane concentrated moments is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in a closed form for the case in which there is a single crack in an infinite plate subjected to symmetric concentrated moments. 相似文献
8.
9.
This work investigates nonlinear characteristics of a circular laminated plate. A nonparametric identification method based on the Hilbert transform is applied to identify the nonlinear system. The results demonstrate that the force–displacement curve has a soft nonlinear characteristic under small displacements and a hard nonlinear characteristic under large displacements. The force–velocity curve also has a soft nonlinear characteristic. A circular isotropic plate is treated to test the method. The force-state method is adopted to confirm the identification results. The effects of the plate diameter are examined. A combination of a cubic polynomial and a hyperbolic tangent function is proposed to fit the experiment data. The fitting results are verified by time domain simulations under random excitations. The work illustrates some novel nonlinear characteristics in transverse vibration of a circular laminated plate via a nonlinear system identification process. 相似文献
10.
求解饱和半空间上弹性圆板固结沉降的积分方程 总被引:1,自引:0,他引:1
本文采用解析方法分析了弹性圆板在饮和半空间上的固结沉降。考虑弹性圆板与饮和半空间的接触面上无摩擦力,且饱和半空间表面为全部透水的。运用Biot固结理论和积分方程技术,在Laplace变换域上建立了弹性圆板固结沉降的对偶积分方程,并化此对偶积分方程为第二类Fredholm积分方程。通过对其核函数的有效数值发得到第二类Fredholm积分方程的解,再利用Lapace反演技术获得弹性板在时间域中的固结沉 相似文献
11.
A comprehensive treatment of fracture of functionally graded materials (FGMs) is provided. It is assumed that the material
properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces.
By using a laminated composite plate model to simulate the material non-homogeneity, an algorithm for solving the system based
on Laplace transform and Fourier transform techniques is presented. Unlike earlier studies that considered certain assumed
property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with
arbitrarily varying material properties. Transient thermal stresses are presented.
Project supported by the National Natural Science Foundation of China (Nos 10102004 and 19902003). 相似文献
12.
This paper deals with the determination of temperature distribution and thermal deflection function of a thin circular plate with the stated conditions. The transient heat conduction equation is solved by using Marchi-Zgrablich transform and Laplace transform simultaneously and the results of temperature distribution and thermal deflection function are obtained in terms of infinite series of Bessel function and it is solved for special case by using Mathcad 2007 software and represented graphically by using Microsoft excel 2007. 相似文献
13.
14.
单边自由的固支岩板黏弹性行为分析及其应用 总被引:2,自引:0,他引:2
利用黏弹性理论对单边自由的固支岩板的黏弹性力学行为进行了分析研究,重新导出了相空间中黏弹性参数的变换关系式,并利用此式建立了单边自由的固支岩板的广义Kelvin黏弹性分析格式,将其应用于某层状岩体洞室顶板的变形特性分析.计算表明,其与实际勘察结果比较接近,可供工程实际应用参考. 相似文献
15.
Zhang Shanyuan Wang Tiefeng 《Acta Mechanica Solida Sinica》1994,7(4):334-346
A study is presented for the large deflection dynamic response of rigid-plastic circular plate resting on potential fluid under a rectangular pressure pulse load.By virtue of Hankel integral transform technique,this interaction problem is reduced toa problem of dynamic plastic response of the plate in vacuum.The closed-formsolutions are derived for both middle and high pressure loads by solving the equationsof motion with the large deflection in the range where both bending moments andmembrane forces are important.Some numerical results are given. 相似文献
16.
We present a methodology correlating the group velocity of guided plate waves to temperature in anisotropic silicon substrate.
The model is developed through numerical solution and manipulation of the dispersion relations, while elastic constants and
plate thickness are treated as functions of temperature. Analytical results demonstrate that adequate thermal resolution is
provided by both the lowest-order antisymmetric and symmetric dispersive Lamb wave modes to serve as an effective diagnostic
in a noncontact thermometry scheme applicable during rapid thermal processing of silicon waters. Validation is made through
a combination of experimentation using laser-generated ultrasound in silicon wafers and analysis employing the Gabor wavelet
transform to extract frequency- and temperature-dependent group velocities from the dispersive Lamb waves. 相似文献
17.
利用刚性圆板表面各点位移相等,并结合刚性圆板与地基表面的位移相容条件与光滑接触条件,经由Hankel变换,推导出了刚性圆板与分层地基表面接触应力的对偶积分方程;求解该对偶积分方程,再由多层地基应力与位移的传递矩阵解,并经Hankel逆变换,得到了多层地基上轴对称受荷刚性圆板问题的解.编制了计算程序,并进行了数值分析与计算.计算结果表明:对均匀地基而言,实际工程的计算分析可只考虑4倍刚性圆板直径以内深度范围内的应力与位移;而地基的分层性对地基的位移和应力有着较大的影响,简单地将均匀地基的结论推广到分层和非均匀地基是不恰当的. 相似文献
18.
In this paper the low frequency vibrations of an elastic circular plate on a saturated poroelastic half space are studied by the analytical method. First the governing equations of the dynamic problem for a saturated poroelastic medium are solved by means of Hankel transform. Then the dual integral equations of vertical forced vibration of an elastic plate on saturated poroelastic half space are established according to the mixed boundary-valued condition. By applying Abel transform the dual integral equations are reduced to a Fredholm integral equation of the second kind. Numerical examples are given at the end of the paper. 相似文献
19.
多孔饱和半空间上弹性圆板的动力分析 总被引:6,自引:2,他引:6
用解析方法研究多孔饱和半空间上弹性圆板的低垂直振动,首先用Hankel变换求解多孔饱和介质动力问题控制方程,然后按混合边值条件建立多孔饱和半空间上弹性板的垂直振动的对偶积分方程,用Abel变换化对偶积分方程为第二类Fredholm积分方程,并给出了数值算例。 相似文献
20.
The theoretical solutions of eigenfrequencies and vibration modes of a rectangular thin plate on an elastic foundation with completely free boundary are derived by using a double finite cosine integral transform method. In the analysis procedure, the elastic foundation is regarded as a Winkler elastic foundation model. Because the basic dynamic elasticity equations of the thin plate on elastic foundation are only used, it is not needed to select the deformation function arbitrarily. Therefore, the solution developed in the present paper is more reasonable and more accurate. To prove the correctness of the solutions, numerical results obtained using the present solutions are compared with those in the literatures. 相似文献