Markov Approximation to Transient Vibration

Abstract

The response of a lightly damped single‐degree‐of‐freedom oscillator to a random excitation with an evolutionary broad‐band power spectrum is considered. Analytical solutions are given for the transition, joint, and marginal probability densities of a Markovian approximation of the response amplitude. Digital data generated by extensive simulations of the response amplitude statistics are presented as well. These data are discussed in context with an assessment of the reliability of the developed analytical solutions.