Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

doi:10.1007/s10483-018-2399-9

摘要/Abstract

摘要： This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.

关键词: singular perturbation, reaction diffusion equation, delay, upperand lower solutions, uniformly validity, reticulated shallow spherical shell, nonlinear free vibration, transverse shear effect, asymptotical iteration method, amplitude-frequency relation

Abstract: This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.

Key words: singular perturbation, reaction diffusion equation, delay, upperand lower solutions, uniformly validity, amplitude-frequency relation, nonlinear free vibration, reticulated shallow spherical shell, transverse shear effect, asymptotical iteration method

中图分类号:

74K25
74H45

Rong WANG, Guohua NIE. Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1825-1836.

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