Li, Qiang

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.

The motion stability of long-span bridges under turbulent wind is studied. A new stochastic theory, developed on the basis of a new wind turbulence model, is applied to experimentally measured bridge deck models to determine the stochastic stability boundaries. The new turbulence model has a finite mean-square value and a versatile spectral shape, and is capable of closely matching a target spectrum, such as the Dryden or the von Karman spectrum, by changing the parameters of the model. The bridge motion is represented as a linear system of single degree of freedom in torsion. A bridge is generally subject to two types of wind loads: the buffeting loads and the self-excited loads. Only the self-excited loads are considered in the investigation, since the buffeting loads, which appear as inhomogeneous terms in the differential equation of motion, do not affect the motion stability of a linear system. In the absence of turbulence, the onset of flutter instability occurs at a critical wind velocity at which a pair of complex-conjugate eigenvalues of the combined structural-fluid system becomes purely imaginary. The corresponding eigenvectors describe the interaction between the structure and the surrounding fluid. Upon the introduction of turbulence, the composition of the structural and fluid components is changed. Since the turbulence portion of the flow fluctuates randomly in time, a new state of balance between the energy inflow from fluid to structure, and the energy outflow from structure to fluid, can only be reached in the statistical sense, or equivalently, in the sense of long-time average under the ergodicity assumption. It is the random deviation from the deterministic flutter mode that renders either the stabilizing or destabilizing effect possible. The asymptotic sample stability boundary of the motion is obtained. The aerodynamic constants for the theoretical analysis are measured experimentally in a forced vibration test conducted in a water channel, with water substituting for air as the working fluid. For a particular bridge deck model, the computed stability boundary shows that the presence of turbulence in the wind flow can be either stabilizing or destabilizing depending on the peak frequency and band-width of the turbulence spectrum.