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

Applied Mathematics and Mechanics(English Edition) 2018年第12期39卷 1825-1836页

作者： Rong WANG Guohua NIE School of Aerospace Engineering and Applied Mechanics Tongji University

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

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Dynamic Stability of Viscoelastic Plates with Finite Deformation and shear effects

引用

Journal of Shanghai University(English Edition) 2002年第2期6卷 115-124页

作者：李晶晶程昌钧张能辉 ShanghaiInstituteofAppliedMathematicsandMechanics andCollegeofSciencesShanghaiUniversityShanghai200072China

Based on Reddy's theory of plates with higher order shear deformations and the Boltzmann superposition principles, the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects. The Galerkin method was applied to simplify the set of equations. The numerical methods in nonlinear dynamics were used to solve the simplified system. It could be seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads. The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelastic plates were investigated.

关键词： viscoelastic plate transverse shear effect stability chaos strange attractor.

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