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1.
P. MAITI P.RAKSHIT S. BANERJEA 《应用数学和力学(英文版)》2011,32(5):635-644
The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged
in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation
by a suitable application of Green's integral theorem in terms of difference of potential functions across the barrier. This
integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and
transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover
parameter. 相似文献
2.
The problem of water wave scattering by a thin circular-arc-shaped plate submerged in infinitely deep water is investigated by linear theory. The circular-arc is not necessarily symmetric about the vertical through its center. The problem is formulated in terms of a hypersingular integral equation for a discontinuity of the potential function across the plate. The integral equation is solved approximately using a finite series involving Chebyshev polynomials of the second kind. The unknown constants in the finite series are determined numerically by using the collocation and the Galerkin methods. Both the methods ultimately produce very accurate numerical estimates for the reflection coefficient. The numerical results are depicted graphically against the wave number for a variety of configurations of the arc. Some results are compared with known results available in the literature and good agreement is achieved. The suitability of using a circular-arc-shaped plate as an element of a water wave lens has also been discussed on the basis of the present numerical results. 相似文献
3.
The present study deals with the surface gravity wave interaction with submerged horizontal flexible porous plate under the assumption of small amplitude water wave theory and structural response. The flexible porous plate is modeled using the thin plate theory and wave past porous structure is based on the generalized porous wavemaker theory. The wave characteristics due to the interaction of gravity waves with submerged flexible porous structure are studied by analyzing the complex dispersion relation using contour plots. Three different problems such as (i) wave scattering by a submerged flexible porous plate, (ii) wave trapping by submerged flexible porous plate placed at a finite distance from a rigid wall and (iii) wave reflection by a rigid wall in the presence of a submerged flexible porous plate are analyzed. The role of flexible porous plate in attenuating wave height and creating a tranquility zone is studied by analyzing the reflection, transmission and dissipation coefficients for various wave and structural parameters such as angle of incidence, depth of submergence, plate length, compression force and structural flexibility. In the case of wave trapping, the optimum distance between the porous plate and rigid wall for wave reflection is analyzed in different cases. In addition, effects of various physical parameters on free surface elevation, plate deflection, wave load on the plate and rigid wall are studied. The present approach can be extended to deal with acoustic wave interaction with flexible porous plates. 相似文献
4.
The problem of water wave scattering by a thin vertical elastic plate submerged in infinitely deep water is investigated here assuming linear theory. The boundary condition on the elastic plate is derived from the Bernoulli–Euler equation of motion satisfied by the plate. This is converted into the condition that the normal velocity of the plate is prescribed in terms of an integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green’s function. The reflection and transmission coefficients are obtained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate and its normal derivative on the plate, which satisfy three simultaneous integral equations, solved numerically. These coefficients are computed numerically for various values of different parameters and are depicted graphically against the wave number for different situations. The energy identity relating these coefficients is also derived analytically by employing Green’s integral theorem. Results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small. 相似文献
6.
Summary This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a homogeneous,
isotropic, viscoelastic, solid sphere immersed in an unbounded viscous, heat-nonconducting, compressible fluid. The dynamic
viscoelastic properties of the spherical scatterer and the viscosity of the surrounding fluid are rigorously taken into account
in the solution of the acoustic-scattering problem. Havriliak–Negami model for viscoelastic material behaviour along with
the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form
solution in form of infinite series. Subsequently, the associated acoustic quantities such as the scattered far-field pressure
directivity pattern, scattered intensity distribution, differential scattering cross section, and the acoustic radiation force
are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to
the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the solid obstacle can be of major
significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established.
Received 15 January 2002; accepted for publication 2 July 2002
The authors wish to sincerely thank professors Daniel Levesque, Roderic Lakes, Yves Berthelot, S. Temkin, and Andrei Dukhin
for valuable and productive consultations on dynamic theory of viscoelasticity and acoustics of (thermo)viscous media. 相似文献
7.
DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT 总被引:2,自引:0,他引:2
The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given. The results obtained demonstrate good agreement with other reported results and show high accuracy. 相似文献
8.
IntroductionCompositematerialconsistingofapiezoelectricphaseandapiezomagneticphasehasdrawnsignificantinterestinrecentyears,duetotherapiddevelopmentinadaptivematerialsystems .Itshowsaremarkablylargemagnetoelectriccoefficient,thecouplingcoefficientbetweenst… 相似文献
9.
Scattering of harmonic elastic waves by a plane interface crack with linear adhesive tips in a layered half space 总被引:1,自引:0,他引:1
In this paper, the scattering of elastic waves by an interface crack with linear adhesive tips in a layered half space is considered. By use of integral transform and integral equation methods, the singular integral equations of this problem are derived, which are transformed into a set of algebraic equations by means of contour integration and Chebyshev polynomials expanding technique. The numerical results of the adhesive region and stress amplitudes are given in this paper. 相似文献
10.
A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely
isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic
induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform,
the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were
gained by making use of Fourier transform and adopting electro-magneto impermeable boundary conditions. The closed form expression
for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations
using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around
the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic
stress intensity factor.
Contributed by SHEN Ya-peng
Foundation item: the National Natural Science Foundation of China (10132010, 50135030)
Biographies: DU Jian-ke (1970∼) 相似文献
11.
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
12.
T. Yokoyama 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(6-7):359-370
Summary A finite element technique is presented for the analysis of one-dimensional torsional plastic waves in a thin-walled tube.
Three different nonlinear consitutive relations deduced from elementary mechanical models are used to describe the shear stress–strain
characteristics of the tube material at high rates of strain. The resulting incremental equations of torsional motion for
the tube are solved by applying a direct numerical integration technique in conjunction with the constitutive relations. The
finite element solutions for torsional plastic waves in a long copper tube subjected to an imposed angular velocity at one
end are given, and a comparison with available experimental results to assess the accuracy of the constitutive relations considered
is conducted. It is demonstrated that the strain-rate dependent solutions show a better agreement with the experimental results
than the strain-rate independent solutions. The limitations of the constitutive equations are discussed, and some modifications
are suggested.
Received 9 February 1999; accepted for publication 28 March 2000 相似文献
13.
Flexural waves are scattered by inclusions in a thin plate. For a single inclusion of arbitrary shape, reciprocity relations are obtained connecting coefficients in circular multipole expansions. Then, a formula for the effective wavenumber in a random arrangement of identical circular inclusions is derived, using the Lax quasi-crystalline approximation. 相似文献
14.
Ming DONG 《应用数学和力学(英文版)》2020,41(7):1105-1124
The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional(2 D) roughness element on the oncoming Tollmien-Schlichting(T-S) modes when th... 相似文献
15.
两层流体中水波在垂直薄板上的反射与透射 总被引:9,自引:1,他引:9
研究在两层流体中表面波模态和内波模态的波浪与半潜式刚性垂直薄板
相互作用的问题. 基于特征函数展开理论,建立了两种模态入射波作用下,半潜式刚性垂直
薄板的反射与透射能量的计算方法,证明了对每一种模态的入射波,另一种模态波浪的反射
与透射能量是相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量,以及作用在其上的
水平波浪力进行了数值计算分析,表明在某个频率范围内,流体的分层效应对这些水动力
量的影响是不可忽视的. 特别地,当薄板的一端位于两层流体的内界面上时,两种模态波浪
的能量转化是最大的. 相似文献
16.
Ya-Pu Zhao 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(1):77-84
Summary The morphological stability of epitaxial thin elastic films on a substrate by van der Waals force is discussed. It is found
that only van der Waals force with negative Hamaker constant tends to stabilize the film, and the lower bound for the Hamaker constant is also obtained for the stability of thin film.
The critical value of the undulation wavelength is found to be a function of both film thickness and external stress. The
charateristic time-scale for surface mass diffusion scales to the fourth power to the wavelength of the perturbation.
Received 4 December 2000; accepted for publication 31 July 2001 相似文献
17.
利用积分变换技术,结合Copson方法,研究了含直线型对称裂纹的一维六方压电准晶对SH波的散射问题。通过求解对偶积分方程,得到声子场、相位子场应力、位移及电场电位移分量的解析解。定义了裂纹尖端应力强度因子及电位移强度因子,给出了电非渗透性条件下应力强度因子及电位移强度因子的解析解。此研究结果对压电准晶材料的工程应用有一定的理论价值。 相似文献
18.
The plane problem of an elliptically reinforced circular hole in an anisotropic plate or laminate 总被引:11,自引:0,他引:11
Summary Within the scope of linear elasticity, the in-plane problem of an anisotropic plate or laminate with a circular hole and
an elliptical hole reinforcement is considered. Arbitrary anisotropic elastic stiffnesses are allowed for the base plate and
the reinforcement material, and for the reinforcement there is no restriction for its elliptical shape and size. The analysis
of the problem is performed by the complex potential method with appropriately chosen series representations inside and outside
the reinforcement region. The derived closed-form solution provides all resultant in-plane stresses and deformations within
and around the hole reinforcement with little computational effort and at high accuracy. The determined solution allows a
proper and effective assessment of hole reinforcements for many technical applications.
Received 26 June 2000; accepted for publication 26 September 2000 相似文献
19.
Summary An exact, three-dimensional analysis is developed for a penny-shaped crack in an infinite transversely isotropic piezoelectric
medium. The crack is assumed to be parallel to the plane of isotropy, with its faces subjected to a couple of concentrated
normal forces and a couple of point electric charges that are antisymmetric with respect to the crack plane. The fundamental
solution of a concentrated force and a point charge acting on the surface of a piezoelectric half-space is employed to derive
the integral equations for the general boundary value problem. For the above antisymmetric crack problem, complete expressions
for the elastoelectric field are obtained. A numerical calculation is finally performed to show the piezoelectric effect in
piezoelectric materials. It is noted here that the present analysis is an extension of Fabrikant's theory for elasticity.
Received 30 August 1999; accepted for publication 1 March 2000 相似文献
20.
M. P. Malezhik I. S. Chernyshenko G. P. Sheremet 《International Applied Mechanics》2007,43(7):767-771
Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular
holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are
used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves
propagate
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 73–78, July 2007. 相似文献