共查询到20条相似文献,搜索用时 31 毫秒
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基于平板小挠度弯曲波动方程,采用摄动方法具有纵向内力作用下的平板开孔弹性波的散射问题进行了研究,得么了传播稳态波时此种平板弯曲波动问题的分析解,分析了均匀纵向内力对弹性波散射结果的影响,作为算例,本文给出了平板圆形开孔的动应力集中系数的数值结果,并对计算结果进行了讨论。 相似文献
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《Wave Motion》2020
Cloaking of a circular cylindrical elastic inclusion embedded in a homogeneous linear isotropic elastic medium from antiplane elastic waves is studied. The transformation or change-of-variables method is used to determine the material properties of the cloak and the homogenization theory of composites is used to construct a multilayered cloak consisting of many bi-material cells. The large system of algebraic equations associated with this problem is solved by using the concept of multiple scattering with wave expansion coefficient matrices. Numerical results for cloaking of an elastic inclusion and a rigid inclusion are compared with the case of a cavity. It is found that while the cloaking patterns for the three cases are similar, the major difference is that standing waves are generated in the elastic inclusion and the multilayered cloak cannot prevent the motion inside the elastic inclusion, even though the cloak seems nearly perfect. Waves can penetrate into and cause vibrations inside the elastic inclusion, where the amplitude of standing waves depend on the material properties of the inclusion but are very much reduced when compared to the case when there is no cloak. For a prescribed mass density, the displacements inside the elastic cylinder decrease as the shear modulus increases. Moreover, the cloaking of the elastic inclusion over a range of wavenumbers is also investigated. There is significant low frequency scattering even if the cloak consists of a large number of layers. When the wavenumber increases, the multilayered cloak is not effective if the cloak consists of an insufficient number of layers. Resonance effects that occur in cloaking of elastic inclusions are also discussed. 相似文献
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Two-dimensional equations for coupled extensional and thickness-stretch waves in an elastic plate are simplified by eliminating the extensional displacements in a systematic manner; the result is a single equation governing thickness-stretch motions. A similar reduction is also performed for coupled extensional, thickness-stretch, and symmetric thickness-shear waves. The procedure is similar to that used in the thickness-shear approximation, wherein the flexural displacement is eliminated from the equations for coupled flexural and thickness-shear motions. The resulting equations are used to discuss the energy-trapped vibration of plates in thickness-stretch modes. 相似文献
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V. S. Shorkin 《Mechanics of Solids》2011,46(6):898-912
The dispersion law ceases to be linear already at ultrasonic frequencies of elastic vibrations of particles as mechanical
perturbation waves propagate through the medium. A variant of the continuum model of an elastic medium is proposed which is
based on the assumption of pair and triplet potential interaction between infinitely small particles; this allows one to represent
the dispersion law with any required accuracy. The corresponding wave equation, which is still linear, can have an arbitrarily
large order of partial derivatives with respect to the coordinates. It is suggested that the results of comparing the representations
of the dispersion law from the elasticity and solid-state physics viewpoints should be used to determine nonclassical characteristics
of the elastic state of the medium. The theoretical conclusions are illustrated with calculations performed for plane waves
propagating through aluminum. 相似文献
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Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates 总被引:2,自引:0,他引:2
S. Papargyri-Beskou D. E. Beskos 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(8):625-635
The governing equation of motion of gradient elastic flexural Kirchhoff plates, including the effect of in-plane constant
forces on bending, is explicitly derived. This is accomplished by appropriately combining the equations of flexural motion
in terms of moments, shear and in-plane forces, the moment–stress relations and the stress–strain equations of a simple strain
gradient elastic theory with just one constant (the internal length squared), in addition to the two classical elastic moduli.
The resulting partial differential equation in terms of the lateral deflection of the plate is of the sixth order instead
of the fourth, which is the case for the classical elastic case. Three boundary value problems dealing with static, stability
and dynamic analysis of a rectangular simply supported all-around gradient elastic flexural plate are solved analytically.
Non-classical boundary conditions, in additional to the classical ones, have to be utilized. An assessment of the effect of
the gradient coefficient on the static or dynamic response of the plate, its buckling load and natural frequencies is also
made by comparing the gradient type of solutions against the classical ones. 相似文献
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受损伤固体中含有的微裂纹或微孔洞往往具有周期性,对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题,它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年。Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题。并推出显式分析结果。本文基于弹性动力学理论,分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况,可采用具有退化核第一类Fredholm积分方程方法分析求解,在求解中给出相应的无量纲数,例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。 相似文献
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S. Papargyri-Beskou A.E. Giannakopoulos D.E. Beskos 《International Journal of Solids and Structures》2010,47(20):2755-2766
Gradient elastic flexural Kirchhoff plates under static loading are considered. Their governing equation of equilibrium in terms of their lateral deflection is a sixth order partial differential equation instead of the fourth order one for the classical case. A variational formulation of the problem is established with the aid of the principle of virtual work and used to determine all possible boundary conditions, classical and non-classical ones. Two circular gradient elastic plates, clamped or simply supported at their boundaries, are analyzed analytically and the gradient effect on their static response is assessed in detail. A rectangular gradient elastic plate, simply supported at its boundaries, is also analyzed analytically and its rationally obtained boundary conditions are compared with the heuristically obtained ones in a previous publication of the authors. Finally, a plate with two opposite sides clamped experiencing cylindrical bending is also analyzed and its response compared against that for the cases of micropolar and couple-stress elasticity theories. 相似文献
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各向异性平板开孔动应力集中问题的研究 总被引:2,自引:0,他引:2
采用各向异性平板弯曲波动理论及摄动方法,对正交各向异性平板开孔弯曲波的散射及动应力集中问题进行了分析研究,得到了此种平板稳态弯曲波动问题的渐近形式的分析解。同时采用保角映射技术,为求解正交各向异性平板开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。 相似文献
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M. Sathyamoorthy 《International Journal of Solids and Structures》1978,14(10):869-880
An approach to the large amplitude free, undamped flexural vibration of elastic, isotropic skew plates is developed with the aid of Hamilton's principle taking into consideration the effects of transverse shear and rotatory inertia. On the basis of an assumed vibration mode of the product form, the relationship between the amplitude and period is studied for skew plates of various aspect ratios and skew angles clamped along the boundaries. It is found that the time differential equation, i.e. modal equation when numerically integrated provides interesting information about the effects of transverse shear and rotatory inertia on aspect ratios and skew angles of thin and moderately thick skew plates both at small and at large amplitudes. 相似文献
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This paper derives the cubic spline beam function from the generalized beam differential equation and obtains the solution of the discontinuous polynomial under concentrated loads, concentrated moment and uniform distributed by using delta function. By means of Kantorovich method of the partial differential equation of elastic plates which is transformed by the generalized function (δ function and σ function), whether concentrated load, concentrated moment, uniform distributed load or small-square load can be shown as the discontinuous polynomial deformed curve in the x-direction and the y-direction. We change the partial differential equation into the ordinary equation by using Kantorovich method and then obtain a good approximate solution by using Glerkin’s method. In this paper there ’are more calculation examples involving elastic plates with various boundary-conditions, various loads and various section plates, and the classical differential problems such as cantilever plates are shown. 相似文献
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Based on the Timoshenko beam theory, the finite-deflection and the axial inertia are taken into account, and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills, the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case, a shock wave solution is given. The small perturbations are further introduced, arising from the damping and the external load to an original Hamilton system, and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform. 相似文献
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The propagation of oscillatory waves through periodic elastic composites has been analysed on the basis of the Floquet theory. This leads to self-adjoint differential equation systems which it was proved convenient to solve by variational methods. Many composites, such as the light-weight high-strength boron-epoxy material, consist of strong reinforcing components in a plastic matrix. The latter can exhibit viscoelastic properties which can have a significant influence on wave propagation characteristics. Replacement of the elastic constant by the viscoelastic complex modulus changes the mathematical structure so that the differential equation system is no longer self-adjoint. However, a modification of the variational principles is suggested which retains formal self-adjointness, and yields variational principles which contain additional boundary terms. These are applied to the determination of wave speeds and mode shapes for a laminated composite made of homogeneous elastic reinforcing plates in a homogeneous viscoelastic matrix for plane waves propagating normally to the reinforcing plates. These results agree well with the exact solution which can be evaluated in this simple case. The variational principles permit solutions for periodic, but otherwise arbitrary variation of material properties. 相似文献
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含孔平板弹性波散射问题的复变函数方法 总被引:1,自引:0,他引:1
本文采用平板弯曲波动理论及复变函数方法,对平板开孔弹性波的散射及动应力集中问题进行了分析研究,得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术,就为主解平板任意形状开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。作为算例,本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果,并对其进行了讨论。 相似文献
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Based on the motion equations of flexural wave in Ambartsumian's plates including the effects of transverse shear deformations,
by using perturbation method of small parameter, the scattering of flexural waves and dynamic stress concentrations in the
plate with a cutout have been studied. The asymptotic solution of the dynamic stress problem is obtained. Numerical results
for the dynamic stress concentration factor in Ambartsumian's plates with a circular cutour are graphically presented and
discussed.
The project supported by the National Natural Science Foundation of China. 相似文献