Abstract
An investigation is described of the concave shape generation mechanism in the displacement and its first derivative (vibration velocity) amplitude probability density functions of the narrow-band random vibration of a non-linear string. Three types of strings are studied in detail, characterized as follows: (1) constant damping factor and non-linear stiffness; (2) the damping factor an even function with respect to the displacement and its first derivative, and non-linear stiffness; (3) the damping factor an even function of the displacement and its first derivative and linear stiffness. It is verified by numerical calculation that for a response sample of relatively long duration (of the order of eight representative “periods” of the oscillation) the generation of the concave shape depends mainly upon (1) the saturation of the amplitude and the growth of higher harmonic oscillation due to the non-linear stiffness or the even function damping, and (2) a jump-phenomenon in the input-output relation.
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 call
