黏弹性圆柱壳计及切变形和转动惯量时的动力学稳定性

B·Kh·艾什马托夫

黏弹性圆柱壳计及切变形和转动惯量时的动力学稳定性

B·Kh·艾什马托夫

塔什干灌溉与土壤改良学院数模与信息技术系,塔什干 100000,乌兹别克斯坦

详细信息

作者简介:
B·Kh·艾什马托夫,副教授,博士(联系人.Tel:+998-712-635016;E-mail:ebkh@mail.ru).

中图分类号: O347.2
计量
- 文章访问数: 3110
- HTML全文浏览量: 154
- PDF下载量: 695
- 被引次数: 0
出版历程
- 收稿日期: 2007-02-15
- 修回日期: 2007-06-26
- 刊出日期: 2007-10-15

Dynamic Stability of Viscoelastic Circular Cylindrical Shells Taking Into Account Shear Deformation and Rotatory Inertia

B. Kh. Eshmatov

Department of Mathematical Modeling and Information Technology, Tashkent Institute of Irrigation and Melioration, Tashkent, 100000, Uzbekistan

摘要

摘要: 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．
- Timoshenko理论 /
- 动力稳定性 /
- 圆柱壳 /
- 黏弹性
Abstract: The problem of dynamic stability of a viscoelastic circular cylindrical shell was discussed accor ding to Timoshenko revised theory,with a ccount of shear de formation and rotatory inertia in the geometrically nonlinear statement.Proceeding by Bubnov-Galerkin method in combination with numerical method based on the quadrature formula the problem was reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.For wide range of variation of physical-mechanical and geometrical parameters,dynamic behavior of the shell was studied.The influence of visco elastic properties of the material on the dynamical stability of the circularcy lindrical shell is shown.Results obtained using different theories are compared.
- Timoshenko theory /
- dynamic stability /
- cylindrical shell /
- viscoela sticity

HTML全文

参考文献(29)

[1]	Volmir A S.The Nonlinear Dynamics of Plates and Shells[M].Moscow:Nauka, 1972.
[2]	Timoshenko S P.Vibration Problems in Engineering[M].New York: Van Nostrand,1958.
[3]	Uflyand Ya S. Distribution of waves at transverse vibrations of cores and plates[J].Journal of Soviet Applied Mathematics and Mechanics[Translated from Prikladnaya Matemetika i Mekhanika]. ,1948,12(3):287-300.
[4]	Mindlin R D. Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates[J].Journal of Applied Mechanics,1951,19(1):31-8.
[5]	Reissner E. The effect of transverse shear deformation on the bending of elastic plates[J].Journal of Applied Mechanics,1945,12:A69-88.
[6]	Ambartsumyan S A.General Theory of Anisotropic Shells[M].Moscow:Nauka,1974.(in Russian)
[7]	Rzhanitsyn A R.Theory of Creep[M].Moscow:Stroyizdat,1968.(in Russian)
[8]	Il'yushin A A, Pobedrya B E.Fundamentals of the Mathematical Theory of Thermoviscoelasticity[M].Moscow:Nauka,1970.(in Russian)
[9]	Rabotnov Yu N.Elements of the Hereditary Mechanics of Solids[M].Moscow: Nauka, 1977.(in Russian)
[10]	Shirakawa K.Effects of shear deformation and rotatory inertia on vibration and buckling of cylindrical shells[J].Journal of Sound and Vibration,1983,91(3):425-37. doi: 10.1016/0022-460X(83)90289-4
[11]	Bogdanovich A E.Nonlinear Dynamic Problems for Composite Cylindrical Shells[M].New York: Elsevier Science Publishers Ltd,1993.
[12]	Awrejcewicz J, Krys’ko V A.Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells.Applications of the Bubnov-Galerkin and Finite Difference Numerical Methods[M].Berlin: Springer-Verlag, 2003.
[13]	Okazaki A, Tatemichi A. Damping properties of two-layered cylindrical shells with an unconstrained viscoelastic layer[J].Journal of Sound and Vibration,1994,176(2):145-61. doi: 10.1006/jsvi.1994.1365
[14]	程昌钧，张能辉.轴压作用下粘弹性柱壳的动力学行为[J].应用数学和力学，2001,22(1):1-8.
[15]	Kozlov V I,Karnaukhova T V.Basic equations for viscoelastic laminated shells with distributed piezoelectric inclusions intended to control nonstationary vibrations[J].Journal of International Applied Mechanics,2002,38(10):1253-60. doi: 10.1023/A:1022266614651
[16]	Koltunov M A.Creep and Relaxation[M].Moscow: Visshaya shkola,1976.(in Russian)
[17]	Potapov V D.Stability of Stochastic Elastic and Viscoelastic Systems[M].Chichester (England): Wiley, 1999.
[18]	Badalov F B, Eshmatov Kh, Yusupov M. About some methods of the decision of systems integro-differential equations meeting in problems viscoelasticity[J].Journal of Soviet Applied Mathematics and Mechanics[Translated from Prikladnaya Matemetika i Mekhanika]. ,1987,51:867-71.
[19]	Badalov F B,Eshmatov Kh.The brief review and comparison of integrated methods of mathematical modeling in problems of hereditary mechanics of rigid bodies[J].International Journal of Electronic Modeling,1989,11(2):81-90.
[20]	Badalov F B,Eshmatov Kh. To research of nonlinear vibrations of viscoelastic plates with initial imperfections[J].Journal of Soviet Applied Mechanics[Translated from Prikladnaya Mekhanika]. ,1990,28(8):99-105.
[21]	Badalov F B, Eshmatov Kh, Akbarov U I. Stability of a viscoelastic plate under dynamic loading[J].Journal of Soviet Applied Mechanics[Translated from Prikladnaya Mekhanika]. ,1991,27(9):892-99.
[22]	Verlan A F, Eshmatov B Kh. Mathematical simulation of oscillations of orthotropic viscoelastic plates with regards to geometric nonlinearity[J].International Journal of Electronic Modeling,2005,27(4):3-17.
[23]	Eshmatov B Kh.Dynamic stability of viscoelastic plates at growing compressing loadings[J].Journal of Applied Mechanics and Technical Physics,2006,47(2):165-75.
[24]	Eshmatov B Kh.Nonlinear vibration analysis of viscoelastic plates based on a refined Timoshenko theory[J].International Applied Mechanics,2006,42(5):596-605. doi: 10.1007/s10778-006-0127-7
[25]	Eshmatov B Kh. Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates[J].Journal of Sound and Vibration,2007,300:709-26. doi: 10.1016/j.jsv.2006.08.024
[26]	Eshmatov B Kh. Nonlinear vibrations of viscoelasftic cylindrical shells taking into account shear deformation and rotatory inertia[J].International Journal of Nonlinear Dynamics,2007.
[27]	Eshmatov B Kh, Khodjaev D A. Nonlinear vibrations and dynamical stability of viscoelastic cylindrical panel with concentrated masses[J].International Journal of Acta Mechanica,2007，190(1/4):165-183. doi: 10.1007/s00707-006-0418-4
[28]	Eshmatov B Kh. Nonlinear vibrations of viscoelastic orthotropic cylindrical shells in view of propagation of elastic waves[J].Materials of XVII Session of the International School on Models of Mechanics of the Continuous Environment,July,4-10,Kazan,2004,186-91.(in Russian)
[29]	Eshmatov B Kh. Nonlinear vibrations of viscoelastic orthotropic plates from composite materials[A].Third M I T.Conference on Computational Fluid and Solid Mechanics[C].June 14-17,Boston:the Massachasetle Institue of Technology (USA),2005.