研究了超声速流中粘弹性夹层梁的稳定性。对夹层梁阻尼层分别采用Kelvin模型本构关系与Maxwell模型本构关系, 根据微元受力平衡及力矩平衡原理得到两种粘弹性模型本构关系的夹层梁在超声速气动力下的振动控制方程。使用Galerkin离散方法得到两种模型振动方程的特征根。对比分析了两种粘弹性模型对夹层梁振动频率及振动稳定性的影响。计算结果显示, 在一定的气动力下, 夹层梁因不同阶频率的耦合而产生颤振;对夹层梁阻尼层选择不同粘弹性模型本构关系不会对颤振点及颤振的发散产生明显影响。
Stability of the rectangular sandwich beam with viscoelastic core is studied in this paper.Two governing equations are obtained resulted from the relationship between force-equilibrium and moment-equilibrium by using Kelvin and Maxwell model.The Galerkin method is employed to investigate the stability and oscillation of the beam when it is in supersonic flow.The effects of the two models on its frequency and stability have been compared and analyzed.Results show that flutter occurs at an internal resonance point, where two order natural frequencies couples.The amplitude of flutter is independent of the viscoelastic model of the core.
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