简支梁随机振动问题的简化解法

通过静力分析精确地确定梁的振型,将具有无限自由度的连续体系的随机振动问题归结为广义单自由度振动问题,计算了Bernoulli-Euler梁和Timoshenko梁的对应于广义坐标的广义质量、广义阻尼系数、广义刚度、广义荷载等物理特性,确定了随机均布荷载的功率谱密度,在此基础上推导出了激励作用下两种梁的最大位移、最大应力的峰值功率谱密度。经与有关文献比较表明,该方法产生的误差极小,却概念清楚,步骤简便,并易于为一般的工程技术人员所掌握,对于不是太复杂的结构进行分析本方法具有实际的指导意义。

Simplified solution to the random vibration problem of simply supported beam

First,the mode shape is determined precisely by static analysis,so that the random vibration problem with infinite DOF is transformed into the problem with a generalized SDOF.After this,the physical properties including the generalized mass,generalized damp coefficient,generalized stiffness,and generalized load,corresponding to the Bernoulli-Euler beam and Timoshenko beam respectively,are calculated.Then,the power spectral density of input stochastic uniform loads is determined.Based on this,the peak power ...