Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells

WANG Yong-gang; DAI Shi-liang

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(4): 391-399

WANG Yong-gang, DAI Shi-liang. Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells[J]. Applied Mathematics and Mechanics, 2004, 25(4): 391-399.

Citation:

WANG Yong-gang, DAI Shi-liang. Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells[J]. Applied Mathematics and Mechanics, 2004, 25(4): 391-399.

Citation:

WANG Yong-gang, DAI Shi-liang. Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells[J]. Applied Mathematics and Mechanics, 2004, 25(4): 391-399.

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Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells

WANG Yong-gang¹,
DAI Shi-liang²

1.
Department of Applied Mechanics, China Agricultural Univeristy, Beijing 100083, P. R. China;

Received Date: 2002-01-29
Rev Recd Date: 2003-10-21
Publish Date: 2004-04-15

Abstract

Abstract

The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied Based on the la be deflection theories of von-kûrnûn and the theory of thermoelasticity,the whole governing equations and their simplified type are derived The time-spatial variables xe separated by Galerlari's technique,thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation.By means of regular perturbation method and multiple-scales method,the first order approximate analytical solution for chxacterislic relation of frequency vs amplitude pararreters along with the decay rate of ampfitude are obtained,and the effects of different geomdric parameters and coupling factors as well as boundary conditions on thermoelaslically coupled nonlinear vibration behaviors are discussed.
- shallow spherical shell,
- shallow conical shell,
- thermoelastically coupled,
- nonlinear vibration,
- perturbation method

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References(10)

References

[1]	Varadan T K, Pandalai K A V. Nonlinear flexural oscillation of orthotropic shallow spherical shells[J].Computers and Structures,1978,9(5):417—425. doi: 10.1016/0045-7949(78)90128-1
[2]	王永岗，王新志，宋慧芳.静载荷作用下正交各向异性旋转扁壳的非线性自由振动[J].应用数学和力学，1997,18(6):545—550.
[3]	Boley B A, Barber A D. Dynamic response of beams and plates to rapid heating[J].Journal of Applied Mechanics,1957,24(5):413—425.
[4]	Nowacki W.Dynamic Problems of Thermoelasticity[M].Leyden, The Netherlands: Sijthoff & Noordhoff International Publishers,1975，123—262.
[5]	Chang W P, Wan S M. Thermomechanically coupled nonlinear vibration of plates[J].International Journal of Nonlinear Mechanics,1986,21(5):375—389. doi: 10.1016/0020-7462(86)90021-1
[6]	Trajkovski D, Bitola T F, Lola I R,et al.A coupled problem of thermoelastic vibrations of a circular plate with exact boundary conditions[J].Mechanics Research Communications,1999,26(2):217—224. doi: 10.1016/S0093-6413(99)00016-6
[7]	Praveen G N, Reddy J N. Nonlinear transient thermoelastic analysis functionally graded ceramic-metal plates[J].International Journal of Solids and Structures,1998,35(33):4457—4476. doi: 10.1016/S0020-7683(97)00253-9
[8]	Tauchert T R. Thermally induced flexure, buckling and vibration of plates[J].Applied Mechanics Reviews,1991,48(8):347—359.
[9]	Khdier A A, Ragab M D, Reddy J N. Thermal effects on the response of cross-ply laminated shallow shells[J].International Journal of Solids and Structures,1992,29(5):653—667. doi: 10.1016/0020-7683(92)90059-3
[10]	钱伟长.变分法及有限元[M].北京：科学出版社,1980,535—565.