二维薄板在超音速气流作用下的热弹性颤振
详细信息Thermoelastic Flutter of a Two-Dimensional Thin Plate in Supersonic Airflow
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摘要:根据von-Karman几何非线性应变位移关系建立了二维薄板在超音速气流作用下的非线性动力学模型,其中气动力根据一阶准静态活塞理论计算.用假设模态法和伽辽金方法使方程离散化,然后用Runge-Kutta方法计算.分析结果用分叉图和相图描述.结果表明,温度效应降低了板的稳定性;随动压增大,系统经历稳定运动、周期运动和混沌运动状态.Abstract:A nonlinear dynamic model for a two-dimensional thin plate in supersonic or hypersonic airflow was derived using the von-Karman’s geometrical nonlinear strain-displacement relation.In model,the first order piston theory is used to simulate the aerodynamic load.The equations in the model were discretized by the assumption mode method and the Galerkin approach,and solved by the Runge-Kutta numerical method.The results were illustrated by bifurcation and phase-plane diagrams.These results indicate that temperature decreases the stability of the plate,and that as the dynamic pressure increases the motion of the system changes from steady state to periodic state,then to chaotic state.
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