A unified approach to two types of evolutionary random response problems in engineering
A unified approach to two types of evolutionary random response problems in engineering
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DOI：
10.1007/s004190050134
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发表时间：
1997-10
影响因子：
2.8
通讯作者：
T. Fang;M. Sun
中科院分区：
文献类型：
--
作者：
T. Fang;M. Sun
结构对地震激励的响应和车辆对道路起伏的响应是工程中两个典型的演化随机问题。这两种演化随机激励都可以被认为是从平稳随机激励演化而来的，尽管是通过两种完全不同的方式。前者可以通过线性时变系统对平稳随机过程进行滤波得到，而后者可以通过对平稳随机过程的变元进行非线性变换而得到。然而，这两种类型的激励引起的响应问题有许多共同之处。通过引入“演化频率响应”的概念，可以统一、简洁地得到这两个问题的响应演化谱的表达式，类似于平稳随机问题的输入/输出功率谱关系。对于这两个进化随机问题，求解过程都是相同的，但进化频率响应的表达式是不同的。此外，演化频率响应可以解释为系统在某些确定性演化简谐激励下的暂态响应。从这个意义上讲，演化随机响应问题可以归结为确定性响应问题。基于复模态分析，给出了求解这两个响应问题的统一方法。该方法可以应用于任何线性时不变系统，无论它们是否是对称的，也不管它们是否具有经典的阻尼性。如果配合统计线性化技术，该方法有望应用于非线性系统。据作者所知，这两类进化随机响应问题的统一方法在文献中是第一次报道。
Response of structures to earthquake excitations and response of vehicles to road undulations are two typical evolutionary random problems in engineering. Both kinds of the evolutionary random excitations can be regarded as evolved from stationary random excitations, though through two utterly different ways. The former one may be obtained by filtering a stationary random process through a linear time-dependent system, while the latter one may result from nonlinear transformations of the argument of a stationary random process. However, the response problems due to both types of excitations have much in common. By introducing the concept of “evolutionary frequency response”, the expressions of the response evolutionary spectra for both problems can be obtained in a unified, concise way, similar to the input/output PSD relationship in a stationary random problem. For both the evolutionary random problems, the solution procedures are all the same, but the expressions for evolutionary frequency responses are different from each other. Moreover, the evolutionary frequency responses may be interpreted as transient responses of the system subject to certain deterministic evolutionary harmonic excitations. In this sense, an evolutionary random response problem can be reduced to a deterministic response problem. Based on the complex modal analysis, a unified approach to these two response problems is derived here. The method can be applied to any linear time-invariant systems, whether they are symmetrical or not, and whether they are classically damped or not. And the method might be hopefully applied to nonlinear systems, if the statistical linearization technique is accompanied. To the knowledge of the authors, this unified approach to two types of evolutionary random response problems is the first time reported in literature.