Random vibration--Mathematical models

The phenomenon of flow-induced vibration is found in many
engineering systems. The fluid flow generates forces on the
structure that cause motion of the structure. In turn, the
structural motion changes the angle of attack between the flow and
the structure, hence the forces on the structure. Furthermore,
turbulence generally exists in a natural fluid flow; namely, the fluid
velocity contains a random part. Thus, the problem is formulated as
a nonlinear system under random excitations.
This thesis is focused on one type of motion known as
galloping. A mathematical model for the motion of an elastically
supported square cylinder in turbulent flow is developed. The
physical nonlinear equation is converted to ideal stochastic
differential equations of the Ito type using the stochastic averaging
method. The probability density for the motion amplitude and the
values for the most probable amplitudes are obtained for various
mean flow velocities and turbulence levels.