CONTROL OF FLUTTER IN BRIDGES

In recent years there has been increasing interest in the application of modern control theory to the problem of vibration suppression in civil structures. The loads on such structures can depend on the environment. For example, the motion of a flexible suspension bridge, such as the original Tacoma Narrows Bridge [Ref. 1], can include unsteady aerodynamic forces. The motion can be described by two partial differential equations for bending and torsional vibration [Ref. 2], with the airstream velocity V as a parameter. The stability of motion is governed by the real part of the system eigenvalues, where the eigenvalues depend on V. For V = 0, the system is self-adjoint [Ref. 3] and the eigenvlaues consist of pairs of mere imaginary complex conjugates. For small V, the eigenvalues have negative real parts, so that the motion is asymptotically stable. As V increases, some real parts can turn positive, rendering the system unstable. The air speed corresponding to zero real part is known as the critical speed V er. If the critical speed corresponds to a value for which the imaginary part of an eigenvalue is different from zero, the structure is said to be in flutter condition [Ref. 3].