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Maria Luisa Tonon 《Journal of Elasticity》2002,69(1-3):15-39
This paper deals with the propagation of acceleration waves in constrained linear elastic materials, within the framework
of the so-called linearized finite theory of elasticity, as defined by Hoger and Johnson in [12, 13]. In this theory, the
constitutive equations are obtained by linearization of the corresponding finite constitutive equations with respect to the
displacement gradient and significantly differ from those of the classical linear theory of elasticity. First, following the
same procedure used for the constitutive equations, the amplitude condition for a general constraint is obtained. Explicit
results for the amplitude condition for incompressible and inextensible materials are also given and compared with those of
the classical linear theory of elasticity. In particular, it is shown that for the constraint of incompressibility the classical
linear elasticity provides an amplitude condition that, coincidently, is correct, while for the constraint of inextensibility
the disagreement is first order in the displacement gradient. Then, the propagation condition for the constraints of incompressibility
and inextensibility is studied. For incompressible materials the propagation condition is solved and explicit values for the
squares of the speeds of propagation are obtained. For inextensible materials the propagation condition is solved for plane
acceleration waves propagating into a homogeneously strained material. For both constraints, it is shown that the squares
of the speeds of propagation depend by terms that are first order in the displacement gradient, while in classical linear
elasticity they are constant.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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For infinite perfectly elastic Mooney materials, nonlinear plane waves are examined in both two and three dimensions. In two
dimensions, longitudinal and shear plane waves are examined, while in three dimensions, longitudinal and torsional plane waves
are considered. These exact dynamic deformations, applying to the incompressible perfectly elastic Mooney material, can be
viewed as extensions of the corresponding static deformations first derived by Adkins [1] and Klingbeil and Shield [2]. Furthermore,
the Mooney strain-energy function is the most general material admitting nontrivial dynamic deformations of this type. For
two dimensions the determination of plane wave solutions reduces to elementary mathematical analysis, while in three dimensions
an integral of the governing system of highly nonlinear ordinary differential equations is determined. In the latter case,
solutions corresponding to particular parameter values are shown graphically.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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We demonstrate that it is expedient to use the complete expansion of the potential in terms of strain gradients for materials whose deformation is described by Murnaghan's potential. The cubic terms are retained in the constitutive equations, in addition to the classical quadratic terms. An analysis of the nonlinear system of wave equations reveals that the third harmonics can be generated. As an example, the nonlinear interaction of plane waves is analyzed for the following three cases of waves entering a medium: (i) a longitudinal wave, (ii) a vertically polarized transverse wave, and (iii) vertically and horizontally polarized transverse waves 相似文献
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M. Destrade 《Journal of Elasticity》1999,55(2):163-166
It is proved that elliptically polarized finite-amplitude inhomogeneous plane waves may not propagate in an elastic material
subject to the constraint of incompressibility. The waves considered are harmonic in time and exponentially attenuated in
a direction distinct from the direction of propagation. The result holds whether the material is stress-free or homogeneously
deformed.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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Waves mentioned in the title were revealed in composite materials that are described by the microstructural theory of the second order — the theory of two-phase mixtures. For harmonic periodic waves, a mixture is always a dispersive medium. This medium admits existence of other waves — waves with profiles described by functions of mathematical physics (the Chebyshov–Hermite, Whittaker, Mathieu, and Lamé functions). If the initial profile of a plane wave is chosen in the form of the Chebyshev–Hermite or Whittaker function, then the wave may be regarded as an aperiodic solitary wave. The dispersivity of a mixture as a nonlinear frequency dependence of phase velocities transforms for nonperiodic solitary waves into a nonlinear phase-dependence of wave velocities. This and some other properties of such waves permit us to state that these waves fall into a new class of waves in materials, which is intermediate between the classical simple waves and the classical dispersion traveling waves. The existence of these new waves is proved in a computer analysis of phase-velocity-versus-phase plots. One of the main results of the interaction study is proof of the existence of this interaction itself. Some features of the wave interaction — triplets and the concept of synchronization — are commented on 相似文献
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Propagation of Harmonic Waves Through Fibrous and Porous Elastic Materials of Regular Microstructure
V. T. Golovchan 《International Applied Mechanics》2002,38(10):1178-1200
A presentation is made of the findings on the propagation of free waves through elastic media with a row of evenly spaced cylindrical cavities. To solve the arising boundary-value problems, the strict method proposed earlier by the author is used. Antiplane elastic problems are studied for domains in the form of a plane-parallel layer, a half-space, a space with one infinite row of cylindrical cavities, and a space with a doubly periodic system of cavities. The calculated roots of the dispersion determinant are tabulated. A detailed analysis of the wave field is carried out. The method used is demonstrated to be highly efficient. 相似文献
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A. Montanaro 《Journal of Elasticity》1999,57(1):25-53
By extending the procedure of linearization for constrained elastic materials in the papers by Marlow and Chadwick et al., we set up a linearized theory of constrained materials with initial stress (not necessarily based on a nonlinear theory).
The conditions of propagation are characterized for small-displacement waves that may be either of discontinuity type of any
given order or, in the homogeneous case, plane progressive. We see that, just as in the unconstrained case, the laws of propagation
of discontinuity waves are the same as those of progressive waves. Waves are classified as mixed, kinematic, or ghost. Then we prove that the analogues of Truesdell"s two equivalence theorems on wave propagation in finite elasticity hold for
each type of wave.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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弹性波作用下压电体摩擦接触界面滑移特性分析 总被引:1,自引:0,他引:1
弹性波与压电体摩擦接触界面相互作用会引起界面滑移或分离,滑移和分离位置的分布与外加压力、剪力、电场及入射波的条件有关。应用Fourier分析及matlab软件给出了滑移范围的解,给出了粘着、滑移或分离的判定条件,通过算例分析了滑移和分离出现的影响因素和条件,为工程应用提供了理论依据。 相似文献
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The term fractal was coined by Benoît Mandelbrot to denote an object that is broken or fractured in space or time. Fractals provide appropriate models for many media for some finite range of length scales with lower and upper cutoffs. Fractal geometric structures with cutoffs are called pre-fractals. By fractal media, we mean media with pre-fractal geometric structures. The basis of this study is the recently formulated extension of continuum thermomechanics to such media. The continuum theory is based on dimensional regularization, in which we employ fractional integrals to state global balance laws. The global forms of governing equations are cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order. Using Hamilton??s principle, we derive the equations of motion of a fractal elastic solid under finite strains. Next, we consider one-dimensional models and obtain equations governing nonlinear waves in such a solid. Finally, we study shock fronts in linear viscoelastic solids under small strains. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions and reduce to conventional forms for continuous media with Euclidean geometries upon setting the dimensions to integers. 相似文献
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Anna Ghazaryan Peter Gordon Christopher K. R. T. Jones 《Journal of Dynamics and Differential Equations》2007,19(4):951-966
We study traveling wave solutions arising in Sivashinsky’s model of subsonic detonation which describes combustion processes
in inert porous media. Subsonic (shockless) detonation waves tend to assume the form of a reaction front propagating with
a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity [5]. Moreover, it has been
shown that, when the thermal diffusivity is neglected, the traveling wave is unique. The question of whether the wave is unique
in the presence of thermal diffusivity has remained open. For the subsonic regime, the underlying physics might suggest that
the effect of small thermal diffusivity is insignificant. We analytically prove the uniqueness of the wave in the presence
of non-zero diffusivity through applying geometric singular perturbation theory.
Dedicated to Mr. Brunovsky in honor of his 70th birthday. 相似文献
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We study stationary waves of envelopes in a nonrelativistic electron stream on a fixed ion background. It is shown that the velocity of the stationary wave of an envelope is always equal to the velocity of the unperturbed electron stream. In the adiabatic approximation it is found that each perturbation of the envelopes propagates with velocity of the unperturbed stream. The result is of interest for the theory of nonlinear waves in dispersive media.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 16–23, May–June, 1972. 相似文献