模糊振动理论

The Theory of Fuzzy Vibration

本文首先根据模糊函数的积分,讨论了模糊周期函数的傅里叶级数展开,分析了单自由度系统的模糊强迫振动问题,给出了模糊响应集隶属函数的具体表达式;然后在zadeh定义的模糊变量的基础上,定义了含模糊参数的随机变量和含模糊参数的随机过程。将模糊随机干扰模拟为含模糊参数的随机过程,分析了模糊随机干扰下的振动系统的模糊随机响应。最后由干扰力的期望讨论了模糊随机响应的自相关函数。

In this paper, first according to the integration of fuzzy function, Fourier series expansion of fuzzy cycle function is discussed. The probems of fuzzy forced vibation of single degree of freedom are analysed . The expressions of fuzzy response sets under the jurisdiction of function are given. Then, the random variable and random process with a fuzzy parameter are defined. By simulating the fuzzy random interference as a random process with a fuzzy parameter, the fuzzy random response of vibration systems of the random interference with fuzziness are analysed. Finally, autocorrelation function of the fuzzy random response are discussed by means of expectation of interference force.