共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we consider the propagation of Rayleigh surface waves in a functionally graded isotropic thermoelastic half-space, in which all thermoelastic characteristic parameters exponentially change along the depth direction. The propagation condition is established in the form of a bicubic equation whose coefficients are complex numbers while the analytical solutions (eigensolutions) of the thermoelastodynamic system are explicitly obtained in terms of the characteristic solutions. The concerned solution of the Rayleigh surface wave problem is subsequently expressed as a linear combination of the three eigensolutions while the secular equation is established in an implicit form. The explicit secular equation is written when an isotropic and homogeneous thermoelastic half-space is considered and some numerical simulations are given for a specific material. 相似文献
2.
In this paper we analyze the behavior of plane harmonic waves and Rayleigh waves in a linear thermoelastic material with voids. We take into account the damped effects of the thermal field upon the propagation waves. Consequently, the propagation condition is established in the form of an algebraic equation of 9th degree whose coefficients are complex numbers while the eigensolutions of the thermoelastodynamic with voids system are explicitly obtained in terms of the characteristic solutions. We show that the transverse waves are undamped in time and they are not influenced by the thermal and porous effects while the longitudinal waves are all damped in time and they are coupled with the thermal and porous effects. The related solution of the Rayleigh surface wave problem is expressed as a linear combination of the eigensolutions in concern. The secular equation is established in an implicit form and afterwards an explicit form is written for an isotropic and homogeneous thermoelastic with voids half-space. Furthermore, we use the numerical methods and computations to solve the secular equation for a specific material. 相似文献
3.
The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wave fronts in an elastic material with different tensile and compressive strengths is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The impact conditions on the boundary of the heteromodular sphere are determined that can lead to the formation of a transition zone (a spherical layer of constant density) between the compression and tension regions. 相似文献
4.
The paper presents the results of an investigation on the motion of a spherical particle in a shock tube flow. A shock tube facility was used for studying the acceleration of a sphere by an incident shock wave. Using different optical methods and performing experiments in two different shock tubes, the trajectory and velocity of a spherical particle were measured. Based upon these results and simple one-dimensional calculations, the drag coefficient of a sphere and shading effect of sphere interaction with a shock tube flow were studied. 相似文献
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6.
The nonlinear equations that underlie the analysis of classical Rayleigh waves are derived for the two-dimensional case of
nonlinear elastic deformation described by the Murnaghan model. In addition to the case of presence of both geometrical and
physical nonlinearities, two special cases are considered where one only type of nonlinearity is taken into account. It is
shown that unlike the one-dimensional problems for plane waves where only three types of nonlinear interaction should be allowed
for, the two-dimensional problems should include 24 types of nonlinear interaction. In the case of geometrical nonlinearity
alone, a preliminary analysis of the nonlinear equations is carried out. Second-order equations are derived. The second approximation
includes the second harmonics of the wave itself and its attenuating amplitude and is nonlinearly dependent on the initial
amplitude of the Rayleigh wave and linearly increasing with the distance traveled by the wave 相似文献
7.
Antje Brucks 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(1):33-47
Experimental results are presented on natural convection in a spherical shell of inner and outer radii r
1 = 14 mm and r
2 = 35 mm, with the inner sphere cooled and the outer sphere heated. The fluids filling the shell are two different silicon
oils having Prandtl numbers 39 and 233. Both spheres are fixed together and can be rotated. In the studied regime, both Coriolis
and centrifugal forces become significant. For sufficiently small Rayleigh numbers the resulting flow pattern is axisymmetric
and steady, consisting of a plume descending from the south pole of the inner sphere, and returning in the equatorial regions.
For greater Rayleigh numbers the flow becomes non-axisymmetric, with azimuthal modes m = 2 to 4 arising. We map out the critical Rayleigh number for the onset of these different modes, and consider how they vary
with increasingly rapid overall rotation. Detailed flow measurements are done by converting a standard 2D particle image velocimetry
system into a scanning quasi-3D PIV system. 相似文献
8.
In this paper, the off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid immovable (fixed) sphere is investigated. It is shown here that shifting the sphere off the axis of wave propagation induces a dependence of the scattering on the azimuthal angle. Theoretical expressions for the incident and scattered field from a rigid immovable sphere are derived. The near- and far-field acoustic scattering fields are expressed using partial wave series involving the spherical harmonics, the scattering coefficients of the sphere, the half-conical angle of the wave number components of the beam, its order and the beam-shape coefficients. The scattering coefficients of the sphere and the 3D scattering directivity plots in the near- and far-field regions are evaluated using a numerical integration procedure. The calculations indicate that the scattering directivity patterns near the sphere and in the far-field are strongly dependent upon the position of the sphere facing the incident high-order Bessel vortex beam. 相似文献
9.
《International Journal of Solids and Structures》2003,40(20):5495-5510
Spherical plate-like structures are used in pressure vessels, spherical domes of power plants, and in many other industrial applications. For non-destructive evaluation of such spherical structures, the mechanics of elastic wave propagation in spherical curved plates must be understood. The current literature shows some valuable studies on Rayleigh surface wave propagation in isotropic solids with spherical boundaries. However, the guided wave propagation problem in an anisotropic spherical curved plate, which has not been studied before, is solved for the first time in this paper.The wave propagation, in both isotropic and anisotropic spherical curved plates, is investigated. The differential equations of motion and the stress-free boundary conditions on the inner and outer surfaces of a hollow sphere are approximately solved by a general solution technique. This solution technique was successfully utilized by the authors for solving the wave propagation problem in cylindrical plates, in their earlier works. Dispersion curves for spherical plates made of isotropic aluminum, steel, and anisotropic composite material are presented as well. 相似文献
10.
在球对称拉伸载荷作用下针对空心球涂层复合材料分析了空心球涂层粒子增强复合材料的局部应力场,得到了界面临界脱粘应力的解析表达式.讨论了各相几何参数对非均匀涂层空心球粒子临界脱粘应力的影响,比较了均匀涂层和非均匀涂层的脱粘应力.结果表明:在球对称拉伸下界面脱粘更容易发生在涂层相与基体相界面间,空心球的壁厚和涂层厚度是影响界面临界脱粘应力的重要因素,因而选择适当的空心球、涂层厚度和提高界面粘结能将有利于提高界面的临界脱粘应力. 相似文献
11.
12.
H. B. McClung 《Journal of Elasticity》1991,25(1):75-94
Historically, the vector Navier equation governing the dynamic response of an elastic, homogeneous, isotropic sphere has been solved using the Helmholtz decomposition of the displacement vector. Further, many of the problems in the literature have been restricted to ones involving axisymmetric geometry. In this presentation, the time-dependent Navier equation is solved using a set of vector spherical harmonics which, previously, has been used primarily in quantum mechanics studies but which seems particularly useful in solving asymmetric problems with nonconservative body forces. Expressions for the displacements, strains, and stresses and a discussion of the vibrations of an elastic sphere are given.Part of the material presented here was developed while the author was on a Developmental Leave at the University of Texas at Austin. 相似文献
13.
《Wave Motion》2016
Based on the finite series method, the Gaussian standing or quasi-standing beam is expressed in terms of spherical wave functions and a weighting parameter, which describe the beam shape and location relative to the particle. An expression is derived for the radiation force on a sphere centered on the axis of a Gaussian standing or quasi-standing wave propagating in an ideal fluid. Rigid, fluid, elastic, and viscoelastic spheres immersed in water are treated as examples. In addition, a method is proposed to compute the axial acoustic radiation force when the sphere is translated axially. Results indicate the capability of the proposed method to manipulate and separate spheres based on their mechanical and acoustical properties. The interaction of a Gaussian quasi-standing beam with a sphere can result in periodic axial force under specific operating conditions. The results presented here may provide a theoretical basis for the development of acoustical tweezers in a Gaussian standing beam, which would be useful in micro-fluidic lab-on-chip applications. 相似文献
14.
The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement. 相似文献
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16.
Rajneesh Kumar Geeta Partap 《应用数学和力学(英文版)》2007,28(3):369-383
The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement. 相似文献
17.
Rajneesh Kumar Geeta Partap 《应用数学和力学(英文版)》2006,27(8):1049-1059
The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit, the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically. 相似文献
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19.
This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier–Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi’s iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes. 相似文献
20.
We find a sufficient condition for the existence of surface (Rayleigh) waves based on the Rayleigh-Ritz variational method.
When specialized to a homogeneous half-space, the sufficient condition recovers the known criterion for the existence of subsonic
surface waves. A simple existence criterion in terms of material properties is obtained for periodic half-spaces of general
anisotropic materials. Further, we numerically compute the dispersion relation of the surface waves for a half-space of periodic
laminates of two materials and demonstrate the existence of surface wave band gaps. 相似文献