Abstract
Large classes of stochastic systems of interest to acoustics and vibrations have time delays. The presence of these time delays hinders efforts to provide physical insight into the system behavior, because of the difficulty of finding exact solutions. This paper addresses this issue by presenting exact steady-state solutions for the probability density functions (pdf's) for linear time delayed oscillators subjected to Gaussian excitation of arbitrary correlation. A key parameter influencing these pdf's is shown to be the ratio of mean generalized kinetic energy to the mean generalized potential energy. In a single damped harmonic oscillator this ratio is unity which implies an equi-partition of generalized energy. Time delays cause deviations in the equi-partition of generalized energy which creates regions of preferential total phase and causes the amplitude pdf to shift from a Rayleigh distribution to a Hoyt distribution.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
