Wind-Excited Vibrations of Structures

The possibilities of passive and active control of wind-induced vibrations of structures in civil engineering are presented. The concept of control by means of mechanical and aerodynamic devices is discussed using results of theoretical and experimentel investigations (model tests and full scale examinations).

The effectiveness of structural control and the advantages and disadvantages from engineering point of view will be considered. Case studies will be presented.

A short description of the phenomena of vortex shedding is presented. Strouhal numbers for different cross sections are presented for the calculation of the critical wind speed. The locking-in effect is explained which leads to the correlation consideration which is the basis of a mathematical model for the use in the practical engineering work. The application to cantilevered and simple supported structures is shown.

The prediction of the vortex resonance amplitude is compared with full scale measurements and with two other mathematical models. The effect of aerodynamic devices is explained.

The atmospheric wind is an unsteady, viscous flow field with irregular changes called a turbulent flow. In chapter 2 there are discussed the basic equations of fluid dynamics for such a flow. For characterizing a turbulent flow there are used time averaged quantities of velocity and pressure and of products of the fluctuations of these quantities and power spectra.s, what is described in chapter 3 generally and in the following chapter especially for the atmospheric boundary layer. Since the probability of the occurrence of a wind velocity in a given interval of time is very important for the safety of a structure, there is one section dealing with wind statistics. Chapters 5 and 6 inform about the flow around rigid bluff bodies, pressure distributions and forces caused by the flow. The following chapter deals with the fundamentals for single-degree and multi-degree of freedom linear dynamic systems. Since the interaction of a wind field and a structure is a very complex problem, model experiments are necessary too. The experimental technique in an artificial boundary layer, in an atmospheric wind tunnel, is discussed in the last chapter, including similarity rules and measurement techniques.

Transverse galloping oscillations of a linear dynamic structure are nonlinear due to the effect of the fluid force. As comparisons between theoretical and experimental results show, it is adequate to measure the forces on a model in a steady flow and apply the results for the dynamic system. The differential equations for the system can be solved either by using a polynomial expression for the aerodynamic force or by a numerical solution in the phase-plane. It is shown that the usually applied criterion by Den Hartog is not sufficient for stability. The very important influence of turbulence on the stability is shown for rectangular cross-sections. Theoretical and experimental investigations concerning the influence of yaw on the stability show, that the onset wind velocity increases with increasing yaw angle. If the critical galloping wind speed is close to the resonance wind speed, mutual effects of the two phenomena may occur. A structure with closely spaced modal frequencies may vibrate in a multi-mode way or in one mode only, as shown by changing the mass distribution of a bridge tower.

A general frame of the problem of gust-excited vibrations of structures is given. The treatment is initially developed with reference to a rigid slender cylinder of infinite length immersed in a bi-dimensional wind field. On the basis of this set up are later derived the three classic formulations of the dynamic alongwind, crosswind and torsional vibrations of flexible constructions. General guidelines are also provided about the coupled three-dimensional vibrations of structures as well as other subjects strictly related to gust buffeting and not dealt with in the present note.

The term “flutter” derives from aeronautical practice where it is used to describe an aeroelastic instability in coupled torsion and vertical bending of aircraft wings. The road decks of long span bridges are prone to a related oscillatory response as well as a single-degree-of-freedom torsional instability. These phenomena may result in destructive levels of amplitude and it is essential that the incipient wind speeds for their occurrence be above the maximum values expected at the bridge site. Structural components such as I-beam section deck hangers used in arch bridges are also prone to torsional instability. In this chapter the analytical framework for analysis of the response is discussed and aerodynamic approaches to improving the aerodynamic stability are presented. The effects on response of the free stream turbulence in the atmospheric surface wind layer are described. Attention is focussed on the critical erection phase response of cable-stayed bridges.

Severe aeroelastic problems arise in Wind Engineering as a result of close spacing between parallel, slender structures such as stacks, towers and overhead electric power cables. Oscillation amplitude of the structure can be considerably greater than for single isolated structures. The motion can be caused by vortex shedding, buffeting or aerodynamic instabilities. The effect of proximity on the flow around the structures and on their dynamic response is described. Analytical considerations are discussed and case histories from wind tunnel and full scale observations are presented.