Random vibration

This chapter summarizes the key ideas of linear random vibration. This discipline focuses on determining the response statistics of an oscillator or structure to input forces that are definable only in terms of their statistics. Typical problems include the following: (1) given the power spectrum of the force, find the power spectrum of the response; (2) given the mean value and variance of the force, find the mean value and variance of the response. The methodology is built upon the linear theory of vibration for discrete single- and multi-degree-of-freedom (DoF) systems, and continuous systems. The approaches are essentially the direct method and the modal analysis method. The direct method may also be called a transfer matrix method (see Chapter 2). Modal analysis (see Chapters 3 and 4) has the same benefit in random vibration as is done in deterministic vibration studies: it can be computationally more efficient. A number of examples are given, as are a list of representative references.