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The molecular mechanics (MM) method is used to determine the frequencies and natural vibration shapes and to determine the buckling critical parameters and the postcritical deformation shapes of single-walled carbon nanotubes with twisted ends. The following two variants of the MM method are used: the standard MM method and the mixed method of molecular mechanics/molecular structure mechanics method (MM/MSM). Computer simulation shows that the MM/MSM method allows one to obtain acceptable values of frequencies and natural vibration shapes as well as of critical angles of twist, appropriate buckling modes, and postcritical deformation configurations of nanotubes compared with the same characteristics of nanotube free vibrations and buckling obtained by the standard MM method. 相似文献
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The effect of layers consisting of small particles or asperities on contact surfaces on the deformation of a block medium
as a whole and the failure of the blocks constituting the medium was studied experimentally. The samples were subjected to
quasistatic uniaxial compression perpendicular to the contact surfaces. Numerical modeling was performed of wave propagation
during pulse loading of a pair of blocks having rough surfaces of contact and made of a material with elastic characteristics
close to the characteristics of marble and limestone.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 173–178, May–June, 2007. 相似文献
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We study static and dynamic stability problems for a thin flexible rod subjected to axial compression with the geometric nonlinearity explicitly taken into account. In the case of static action of a force, the critical load and the bending shapes of the rod were determined by Euler. Lavrent’ev and Ishlinsky discovered that, in the case of rod dynamic loading significantly greater than the Euler static critical load, there arise buckling modes with a large number of waves in the longitudinal direction. Lavrent’ev and Ishlinsky referred to the first loading threshold discovered by Euler as the static threshold, and the subsequent ones were called dynamic thresholds; they can be attained under impact loading if the pulse growth time is less than the system relaxation time. Later, the buckling mechanism in this case and the arising parametric resonance were studied in detail by Academician Morozov and his colleagues.In this paper, we complete and develop the approach to studying dynamic rod systems suggested by Morozov; in particular, we construct exact and approximate analytic solutions by using a system of special functions generalizing the Jacobi elliptic functions. We obtain approximate analytic solutions of the nonlinear dynamic problem of flexible rod deformation under longitudinal loading with regard to the boundary conditions and show that the analytic solution of static rod system stability problems in a geometrically nonlinear statement permits exactly determining all possible shapes of the bent rod and the complete system of buckling thresholds. The study of approximate analytic solutions of dynamic problems of nonlinear vibrations of rod systems loaded by lumped forces after buckling in the deformed state allows one to determine the vibration frequencies and then the parametric resonance thresholds. 相似文献
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For the general solution of two-dimensional equations of dynamics of a transverse isotropic medium with the Carrier–Gassmann condition, we give a representation in terms of two resolvent functions satisfying two separate wave equations. The problem of reflection of plane waves from a rigid wall and a free surface is solved. The coefficients of reflection and transformation of the plane waves are found. These formulas yield a solution for isotropic media too. Some special cases are consideredwhere the shapes (amplitudes) of the reflectedwaves are not uniquely determined, but linearly related with the shape of the incident wave. 相似文献
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K. G. Okhotkin A. Yu. Vlasov Yu. V. Zakharov B. D. Annin 《Journal of Applied Mechanics and Technical Physics》2017,58(5):924-932
This paper presents a geometrically nonlinear analytical model of the flexible cylindrical rim of a deployable precision large space antenna reflectors made of shape-memory polymer composites. A nonlinear boundary-value problem for the rim in the deformed (folded) configuration is formulated and exact analytical solutions in elliptic functions and integrals describing the deformation modes of the rim are obtained. Exact analytical solutions based on the geometrically nonlinear model are obtained and can be used to determine preliminary geometric dimensions and optimal shape of the flexible rim along with the estimation of the accumulated energy. 相似文献
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B. D. Annin A. I. Oleinikov K. S. Bormotin 《Journal of Applied Mechanics and Technical Physics》2010,51(4):579-589
Problems of inelastic straining of three-dimensional bodies with large displacements and turns are considered. In addition
to the sought fields, surface forces and boundary displacements have also to be determined in these problems. Experimental
justification is given to the proposed constitutive equations of steady creep for transversely isotropic materials with different
characteristics under tension and compression. Algorithms and results of the finite-element solution of the problem are presented
for these materials. 相似文献