摘要
本文针对楼板振动问题,强调了机器扰力的随机性质,证明了多简谐扰力下楼板上任一点的稳态响应是一符合正态分布的各态历经过程.据此,提出了非数定的分析方法,从而解决了不需进行振幅叠加而直接对楼板各结点稳态响应进行概率分析的问题.分析中采用有限元法建立结构的受迫振动方程,用逐步积分法提取结点稳态响应的样本波,由功率谱密度函数求结点稳态响应的方差,从而对结构的稳态响应进行概率分析.本文揭示了楼板输入与输出的随机性质,并以此观点研究多机器干扰下的楼板振动问题,极大地节省了计算机时,为楼板振动的设计提供了一个合理、有效、适用的方法.
In this paper,the random characters of disturbing loading from vibrations ofmachines are pointed out by dealing with the problem of multi-disturbing loadingfrom floorslab vibration.It is also proved that the steady displacement response atany point on floorslabs under multi-harmonic disturbing loading is an ergodic pro-cess in accordance with normal distribution.On this ground,a method ofnon-deterministic analysis is put forward and the problem is solved so that thesteady response of each joint on floorslabs is statistically analyzed directly withoutthe process of iteration of amplitudes.The finite element method is adopted here to establish vibration equations ofstructures and dynamical loading in the calculation.The step-by-step integrationprocedure is used to get a sample wave of steady response for each joint.Thepower spectrum density function is applied to the calculations of mean variances ofsteady responses of the joints.Accordingly,statistical analysis can be done withsteady responses of jois for structures.The random characters of input and output are dernonstrated in the paper.Theproblem of floorslab vibration under multi-disturbing loading from vibrations ofmachines is studied with a new point of view,and the computing time is decreasedgreatly in this way and a reasonable,efficient and applicable method is devotedto the design of floorslab vibration.
基金
建设部科技发展基金
关键词
多扰力
楼板
振动
非数定分析
multi-disturbing loading
ergodic process
non-deterministic analysis
