研究了均匀各向同性黏弹性梁的横向非线性振动, 该梁在支承两端受到一对轴向压力的作用而发生屈曲, 同时还受到横向简谐激励作用. 通过对屈曲梁的控制方程作坐标变换, 导出了以屈曲平衡位形为坐标轴的扰动方程. 在两端简支边界条件下, 运用Galerkin 方法将其离散化为多自由度非线性振动系统. 在存在内共振的情况下, 应用多尺度法计算得到弱受迫振动时前两阶模态的幅频响应曲线, 并发现了带有平方非线性项的系统所特有的饱和现象.
A nonlinear analysis of the response of a simply-supported viscoelastic buckled beam to a couple of constant axial force and harmonic excitation is resented. The disturbance equation of transverse vibration of the buckled beam is derived from the free governing equation via a coordinate transform. The Galerkin method is applied to truncate the systems to a multiple degrees-of-freedom of nonlinear vibration system. In the presence of internal resonances, a method of multiple scales is developed to obtain the steady-state relationship between the amplitudes in the first two resonant modes in weak forced, and reveal a unique saturation phenomenon in nonlinear system with quadratic items.
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