楼盖振动分析的拟板法

Floor vibration analysis by plate analogy method

从正交异性薄板的振动方程出发,将肋梁楼盖等代为各向异性板,推导了分析楼盖结构振动的拟板法基本公式,求出了楼盖强迫振动的全解、自振频率,以及简谐均布荷载、矩形脉冲荷载、三角形脉冲荷载等三种典型荷载作用下楼盖结构动态响应的稳态解.通过一个典型算例,比较了目前通用的有限元法、各国规范推荐的拟梁法与本文提出的拟板法计算结果的差异,证明拟板法是比拟梁法更合适的楼盖振动分析方法.

Based on the classic theory of elasticity, this paper took ribbed concrete floor as anisotropic plate and deduced a new method named as plate analogy method for analyzing floor vibration. The full solution to forced vibration equation of floor and its self frequency was derived. Stable solutions to dynamic response of floor structure under simple harmonic even distributed load, rectangular impulsive load and triangular impulsive load was also obtained respectively. The results obtained by finite element method, beam analogy method by most codes and plate analogy method by this paper was compared with a typical case study which showed that plate analogy method is more suitable to analyze floor vibration than beam analogy method.