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1.
The problem of propagation of a Lamb elastic wave in a thin plate is considered using the Cosserat continuum model. The deformed state is characterized by independent displacement and rotation vectors. Solutions of the equations of motion are sought in the form of wave packets specified by a Fourier spectrum of an arbitrary shape for three components of the displacement vector and three components of the rotation vector which depend on time, depth, and the longitudinal coordinate. The initial system of equations is split into two systems, one of which describes a Lamb wave and the second corresponds to a transverse wave whose amplitude depends on depth. Analytical solutions in displacements are obtained for the waves of both types. Unlike the solution for Lamb waves, the solution obtained for the transverse wave has no analogs in classical elasticity theory. The solution for the transverse wave is compared with the solution for the Lamb wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 143–150, January–February, 2007. An erratum to this article is available at .  相似文献
2.
Based on a single-domain model of myocardial conduction, isotropic and anisotropic finite element models of the myocardium are developed allowing excitation wave propagation to be studied. The Aliev-Panfilov phenomenological equations were used as the relations between the transmembrane current and the transmembrane potential. Interaction of an additional source of initial excitation with an excitation wave that passed and the spread of the excitation wave are studied using heart tomograms. A numerical solution is obtained using a splitting algorithm that allows the nonlinear boundary-value problem to be reduced to a sequence of simpler problems: ordinary differential equations and linear boundary-value problems in partial derivatives.  相似文献
3.
An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.  相似文献
4.
In the framework of a two-component medium, the phenomenological approach is used to develop a system of constitutive equations describing the thermomechanical behavior of amorphous-crystalline polymers. This model is designed to describe the stress-strain states in the temperature range comprising the intervals of phase and relaxation transitions. The results of numerical experiments demonstrating the possibility of describing the characteristic properties of deformation processes typical of amorphous-crystalline polymers are given.  相似文献
5.
A study is made of waves in a Cosserat continuum, whose strain state is characterized by independent displacement and rotation vectors. The propagation of longitudinal and transverse bulk waves is considered. Wave solutions are sought in the form of wave trains specified by a Fourier spectrum of arbitrary shape. It is shown that if the solution is sought in the form of three components of the displacement vector and three components of the rotation vector which depend on time and the longitudinal coordinate, the initial system is split into two systems, one of which describes longitudinal waves, and the other transverse waves. For waves of both types, dispersion relations and analytical solutions in displacement are obtained. The dispersion characteristics of the solutions obtained differ from the dispersion characteristics of the corresponding classical elastic solutions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 196–203, March–April, 2008.  相似文献
6.
A nondestructive method for monitoring the crack state in reinforced concrete structures based on the recoding of wave processes in these structures under shock actions is proposed. The essence of the method and its possibilities are demonstrated by an example of the study of the behavior of a reinforced concrete beam with a crack at various stages of crack development and repair. Numerical simulation was used to study variations in the wave front characteristics in the crack area. A quantitative criterion was formulated, which permits estimating the concrete integrity or the existence of crack in it and monitoring the variations in the crack state in the process of loading the structure and the crack repair. The criterion is determined as the ratio of the amplitudes of the first half-waves of the acceleration wave front registered in regions on the opposite shores of the crack. The criterion value is independent of the amplitude of the shock action and the beam fixation conditions and is solely determined by the mechanical state of the material used to repair the crack. The criterion adequacy was demonstrated by comparing the results of numerical simulation with experimental data. A cycle of numerical experiments were carried out, which, for each duration of the shock action, permits determining the optimal values of the distance between the pulse application point and the acceleration recording points at which the criterion is most sensitive to the crack state.  相似文献
7.
Experimental results of strain field measurement in polymer composite specimens by Bragg grating fiber optic strain sensors embedded in the material are considered. A rectangular plate and a rectangular plate with “butterfly” shaped cuts are used as specimens. The results of uniaxial strain experiments with rectangular plates show that fiber optic strain sensors can be used to measure the strains, and these results can be used to calculate the calibration coefficients for fiber optic strain sensors. A gradient strain field is attained in a plate with cuts, and the possibility of measuring this field by fiber optic strain sensors is the main goal of this paper. The results of measurements of gradient strain fields in the plate with cuts are compared with the results obtained by using the three-dimensional digital optic system Vix-3D and with the results of numerical computations based on finite element methods. It is shown that the difference between the strain values obtained by these three methods does not exceed 5%.  相似文献
8.
We consider the algorithm of the finite element method for solving two-dimensional problems of nonsymmetric elasticity. We discuss the possibilities of the algorithm and its efficiency by comparing the numerical results with the well-known analytic solutions. We present the results obtained by solving the problem of tension of a plate weakened by a series of holes and the problem of tension for a plate with a central crack. The numerical results thus obtained are considered as an addition to the analytic solutions in the context of experimental justification of couple-stress effects arising under deformation of elastic materials and in the context of solving the identification problem for mechanical constants in nonsymmetric elasticity.  相似文献
9.
10.
In the framework of the nonsymmetric theory of elasticity (the Cosserat contimum), we consider the problem of propagation of a surface acoustic Rayleigh wave in the half-space. The wave is represented as a wave packet of arbitrary form bounded both in the time space and the Fourier space. We assume that the material strain is described by not only the displacement vector but also an independent rotation vector. The general analytic solution of this problem is obtained in displacements. We perform comparative analysis of the obtained solution and the corresponding solution for the classical elastic medium. We introduce and analyze macroparameters characterizing the difference between the stress-strain state and the state predicted by the classical theory of elasticity: the elasticity coefficient, the wave number, and the phase and group velocities. It should be noted that these parameters can be measured experimentally.  相似文献
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