摘要
This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.
论述了一种抑制载重绳索参数激励横向振动的简便方法 .假设绳索底端的质量受到一个垂直简谐激励并忽略载重绳索高阶振型的影响 ,载重绳索的运动方程可以用一个带有立方非线性项的Mathieu方程来描述 .根据Mathieu方程的有关理论 ,在载重绳索系统中 ,当索端质量垂直振动的频率接近绳索横向振动固有频率 2倍时 ,一旦索端质量垂直振动的幅度超过某个临界数值时 ,绳索将产生参数共振 .为了避免这种现象 ,建议在索端质量上加装一个减振器以削减索端质量的垂直振动 ,进而抑制绳索的横向振动 .实验验证了该减振方案的有效性 .
