tailieunhanh - Applied Structural and Mechanical Vibrations 2009 Part 13

Tham khảo tài liệu 'applied structural and mechanical vibrations 2009 part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Summary and comments In the light of the preliminary results on probability and statistics given in Chapter 11 this chapter has considered the subject of random vibrations. Random vibrations arise in a number of situations in engineering practice. More specifically when it is not possible to give a deterministic description of the vibratory phenomenon under investigation but repeated observations show some underlying patterns and regularities we resort to a description in terms of statistical quantities and we speak of a random or stochastic process . This is precisely the subject of Section where we also note that in practical situations the engineer s representation of a random process is an a so-called ensemble . a number of sufficiently long time histories samples which can be used by averaging across the ensemble at specific instants of time to calculate or better estimate all the quantities of interest. Luckily a large number of natural vibratory phenomena have or can be reasonably assumed to have some properties that allow a noteworthy simplification of the analysis. These properties are stationarity and ergodicity Section . There exist different levels of stationarity and ergodicity but broadly speaking the first property has to do with the fact that certain statistical descriptors of the process do not change with time while the second property refers to the circumstance in which a sufficiently long time record can be considered as representative of the whole process. Furthermore ergodicity implies stationarity and in practice when there is evidence that a given process is stationary ergodicity is also tacitly assumed so that we can 1 record only one sufficiently long time history and 2 describe the process by taking time averages along this single sample rather than calculating ensemble averages across a number of different samples the two types of averages being equal because of ergodicity. It should be noted however that the .