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B. Kh. Eshmatov Kh. Eshmatov D. A. Khodzhaev 《Journal of Applied Mechanics and Technical Physics》2013,54(4):578-587
The problem of flutter of viscoelastic rectangular plates and cylindrical panels with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate and panel, the effect of concentrated masses is accounted for using the δ-Dirac function. The problem is reduced to a system of nonlinear ordinary integrodifferential equations by using the Bubnov-Galerkin method. The resulting system with a weakly singular Koltunov-Rzhanitsyn kernel is solved by employing a numerical method based on quadrature formulas. The behavior of viscoelastic rectangular plates and cylindrical panels is studied and the critical flow velocities are determined for real composite materials over wide ranges of physicomechanical and geometrical parameters. 相似文献
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In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special
gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are
proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations.
The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations
with two and three lines of changing type.
相似文献
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Bakhtiyor Eshmatov 《应用数学和力学(英文版)》2007,28(10):1319-1330
The present work discusses the problem of dynamic stability of a viscoelas- tic circular cylindrical shell,according to revised Timoshenko theory,with an account of shear deformation and rotatory inertia in the geometrically nonlinear statement.Pro- ceeding by Bubnov-Galerkin method in combination with a numerical method based on the quadrature formula the problem is reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.For a wide range of vari- ation of physical mechanical and geometrical parameters,the dynamic behavior of the shell is studied.The influence of viscoelastic properties of the material on the dynamical stability of the circular cylindrical shell is shown.Results obtained using different theories are compared. 相似文献
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B. Kh. Eshmatov 《Nonlinear dynamics》2007,50(1-2):353-361
The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined
Timoshenko theory. The problem is solved by the Bubnov–Galerkin procedure combined with a numerical method based on quadrature
formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical
convergence of the Bubnov–Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response
of the cylindrical shell is discussed. The results obtained by various theories are compared. 相似文献
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B. Kh. Eshmatov 《Journal of Applied Mechanics and Technical Physics》2006,47(2):289-297
The dynamic stability problem of viscoelastic orthotropic and isotropic plates is considered in a geometrically nonlinear
formulation using the generalized Timoshenko theory. The problem is solved by the Bubnov-Galerkin procedure combined with
a numerical method based on quadrature formulas. The effect of viscoelastic and inhomogeneous properties of the material on
the dynamic stability of a plate is discussed.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 165–175, March–April, 2006. 相似文献
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Xiaojun Chen Farkhod Eshmatov Wee Liang Gan 《Communications in Mathematical Physics》2011,301(1):37-53
Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincaré duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct a Hopf algebra which quantizes the Lie bialgebra. 相似文献
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根据修正的Timoshenko理论,在几何非线性中考虑了剪切变形和转动惯量,对黏弹性圆柱壳的动力稳定性进行了研究.根据Bubnov-Galerkin法,结合基于求积公式的数值方法,将问题简化为求解具有松弛奇异核的非线性积分-微分方程的问题.针对物理-力学和几何参数在大范围内的变化,研究壳体的动力特性,显示了材料的黏弹性对圆柱壳动力稳定性的影响.最后,比较了通过不同的理论得到的结果. 相似文献