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Nonlinear Vibrations and Stability of an axially moving plate Immersed in Fluid

Acta Mechanica Solida Sinica 2019年第6期32卷 737-753页

作者： Hongying Li Tianyi Lang Yongjun Liu Jian Li Institute of Applied Mechanics College of ScienceNortheastern UniversityShenyang 110819Chinch

In this paper,the nonlinear forced vibrations and stability of an axially moving large deflection plate immersed in fluid are *** on von Karman's large deflec・tion plate theory and taking into consideration the influence of fluid-strueture interaction,axial moving and axial tension,nonlinear dynamic equations are obtained by applying D'Alembert's *** dynamic equations are further discretized into ordinary differential equations via the Galerkin *** frequency-response curves of system are obtained and *** numerical method is used to analyze the bifurcation behaviors of immersed *** show that as the parameters vary,the system displays periodic,multi-periodic,quasi-periodic and even chaotic *** the analysis on global dynamic characteristics of fluid-strueture interaction system,rich and varied nonlinear dynamic characteristics are obtained,and various ways that lead to chaotic motion of the system are further revealed.

关键词： axially moving plate Fluid-strueture interaction Nonlinear vibrations Bifurcations

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Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

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Applied Mathematics and Mechanics(English Edition) 2016年第12期37卷 1647-1668页

作者： Youqi TANG Dengbo ZHANG Mohan RUI Xin WANG Dicheng ZHU School of Mechanical Engineering Shanghai Institute of Technology Third Maintenance Squadron People's Liberation Army 93256 Troops

The dynamic stability of axially accelerating plates is investigated. Longitudi- nally varying tensions due to the acceleration and nonhomogeneous boundary conditions are highlighted. A model of the plate combined with viscoelasticity is applied. In the viscoelastic constitutive relationship, the material derivative is used to take the place of the partial time derivative. Analytical and numerical methods are used to investigate summation and principal parametric resonances, respectively. By use of linear models for the transverse behavior in the small displacement regime, the plate is confined by a viscous damping force. The generalized Hamilton principle is used to derive the govern- ing equations, the initial conditions, and the boundary conditions of the coupled planar vibration. The solvability conditions are established by directly using the method of mul- tiple scales. The Routh-Hurwitz criterion is used to obtain the necessary and sufficient condition of the stability. Numerical examples are given to show the effects of related parameters on the stability boundaries. The validity of longitudinally varying tensions and nonhomogeneous boundary conditions is highlighted by comparing the results of the method of multiple scales with those of a differential quadrature scheme.

关键词： parametric resonance axially moving plate longitudinally varying tension nonhomogeneous boundary condition

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