NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION

Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (4): 331-344.

NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION

李东

Shanghai Institute of Applied Mathematics and Mechanics; Shanghai University of Technology, Shanghai

收稿日期:1991-03-04 出版日期:1992-04-18 发布日期:1992-04-18
基金资助:
Project supported by the National Natural Science Foundation of China

NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION

Li Dong

Shanghai Institute of Applied Mathematics and Mechanics; Shanghai University of Technology, Shanghai

Received:1991-03-04 Online:1992-04-18 Published:1992-04-18
Supported by:
Project supported by the National Natural Science Foundation of China

摘要/Abstract

摘要： A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.

关键词: geometrical nonlinearity, vibration, orthotropy, shallow conical shell, shallow spherical shell

Abstract: A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.

Key words: geometrical nonlinearity, vibration, orthotropy, shallow conical shell, shallow spherical shell

李东. NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(4): 331-344.

Li Dong. NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(4): 331-344.

参考文献

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[4] Singh, P. N., et al., Large amplitude axisymmetric vibrations of moderately thick spherical caps, J. Sound Vib., 20, 3(1972), 269.
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[8] Bucco, D., et al., The dynamic analysis of shallow spherical shells, J. Appl. Mech., 45(1978),690.
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[10] Dumir, P. C., Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps, Acta Mechanica,6O(1986), 121.
[11] Sinharay, G. C., et al., Large amplitude free vibrations of shallow spherical shell and cylindrical shell-a new approach, Int. J. Non-Linear Mech., 20(1985), 69.
[12] Nayfeh,A. H. and D. T. Mook,Nonlinear Oscillations, John Wiley & Sons Inc., New York (1979), 3.
[13] Li, D. and R. H. Liu, Nonlinear vibration of thin circular plates, Adv. Appl. Math. Mech. China, Ed. by Prof., W. Z.Chien,Internationai Academic Publishers, 3 (1990).
[14] Li, D. and R. H. Liu, Application of the modified iteration method to nonlinear vibration of corrugated circular plates, Appl. Math. and Mech.(English Ed.), 11, 1(1990), 13.
[15] Li, D., Large amplitude vibration of thin annular plates, Appl. Math. and Mech.(English Ed.),12, 6 (1991), 583-593.
[16] Li, D., On the nonlinear vibration of corrugated annular plates, Int, Non-Linear Mech., 26(1991).

NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION

NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION

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