Some recent advances in the theory of random vibration

A brief introduction is first given of the history of the technical field of random vibration, tracing back to the works of physicists since the beginning of the twentieth century. This is then followed by an account of more recent developments, with emphasis on nonlinear and quasi-nonlinear systems, and on analytical solutions for the associated Fokker-Planck equation and the generalized Pontryagin equation. The governing equation of a quasi-nonlinear system is linear, but with one or more randomly varying coefficients. The techniques for finding exact probability solutions, approximate probability solutions, conditions for motion stability, and the failure probability and statistics of a system are discussed.