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

作　　者：Rong WANG Guohua NIE 

机构地区：[1]School of Aerospace Engineering and Applied Mechanics, Tongji University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第12期1825-1836,共12页应用数学和力学（英文版）

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.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：nonlinear free vibration reticulated shallow spherical shell transverse shear effect asymptotical iteration method amplitude-frequency relation 

分 类 号：O302[理学—力学] O327