Oscillations In Bridges Research Articles

Existence and stability of large scale nonlinear oscillations in suspension bridges

A nonlinear model of a suspension bridge is considered in which large-scale, stable oscillatory motions can be produced by constant loading and a small-scale, external oscillatory force. Loud's implicit-function theoretic method for determining existence and stability of periodic solutions or nonlinear differential equations is extended to a case of a non-differentiable nonlinearity.

Passive Control of Nonlinear Oscillations in Bridges

Passive Control of Nonlinear Oscillations in Bridges

Active Control of Nonlinear Oscillations in Bridges

This paper shows how to design the parameters of a passive control mechanism in order to keep bridges safe at all possble resonant frequencies caused by nonlinear effects due to midplane stretching. The control mechanism is a king-post truss tendon mechanism. It is basically chosen to shift the natural frequencies of the bridge away from possible resonances. However, the structural parameters of this mechanism can be designed to eliminate or reduce the nonlinear effects on the primary-resonant responses of bridges. The design has been made using a perturbation technique for hinged-hinged single-span bridge.

Wind-induced oscillations of bridges.

Wind-induced oscillations of bridges.

Theoretical analysis of infrasound radiation from an oscillating bridge

As a typical example of the sound radiation caused by the oscillation of a large sized structure, the infrasound radiation from a highway bridge is theoretically analyzed by applying a lifting surface technique. The relation between the bridge oscillation and the corresponding infrasound radiation is made clear quantitatively. By using measured results of the bridge oscillation due to the passage of a vehicle, the infrasound radiated from the bridge is estimated analytically. The results are compared with the measurements, and good agreement is seen. Moreover, it is shown that the reflection of sound at the ground causes both the radiation impedance of the bridge and the radiation pattern of the sound pressure to vary considerably according to the height of the bridge from the ground. Hence the height of the bridge is an important factor which controls sound pressure level ( SPL) near the ground, on which the noise is actually perceived.

Theoretical Analysis of the Sound Radiation Accompanying an Oscillation of Bridge

Theoretical Analysis of the Sound Radiation Accompanying an Oscillation of Bridge

Induced oscillations of highway bridges as a random process

Induced oscillations of highway bridges as a random process

Vibration Frequencies of the Chesapeake Bay Bridge

The aerodynamic causes of suspension bridge oscillations, i.e., vortex theory, flutter theory, and negative slope theory are examined. Thirteen factors to be considered in the design of a suspended span are listed. Frequencies of antisymmetrical and symmetrical modes of vertical oscillation are given and also a minimum frequency in torsional oscillation. Mathematical studies are confined to the suspended span. Seismic studies give a mean fundamental period for the suspended span of 4.5 sec (13.3 cpm) and peak to peak amplitudes as high as 1.0 in. under the influence of a brisk cross wind and heavy traffic. This period agrees well with the calculated period of 4.51 sec (13.31 cpm). Other periods are 2.05 sec (29.27 cpm) and 0.35 sec (171.42 cpm). The cantilever span of extremely stiff design shows a fundamental period of 0.26 sec (231 cpm). The elastic-inertia and aerodynamic characteristics of the Chesapeake Bay Bridge are found to be satisfactory.

Modes and natural frequencies of suspension bridge oscillations

The natural frequencies of potential modes of suspension bridge oscillations constitute basic data required in studies for aerodynamic stability. The formulas presented herein were derived by the author in 1941–1943 and have since been tested, for simplicity and practical usefulness, by fifteen or more years of application in the author's office practice. They have also been independently checked, for validity and accuracy, by others using more difficult formulas involving transcendental (complex or hyperbolic) functions. The author's formulas appear to be the simplest and most practical thus far developed for the calculation of the natural frequencies of all possible modes of suspension bridge oscillations. For convenience of reference and application, these formulas are here assembled, derived and presented in definitive form, together with numerical examples to illustrate their practical application. The numerical examples are based on computations for the Mackinac Bridge.

Aerodynamic Stability of Suspension Bridge under Wind Action

The present paper deals with the forced oscillation of the suspension bridge due to an alternating aerodynamic force and shows the resonance diagram or dynamic magnifier as a function of frequency and wind velocity. The formula for critical wind velocity is also given short and clear.

Discussion of “Peery on Bridge Oscillations”

Discussion of “Peery on Bridge Oscillations”

Closure to “Steinman on Bridge Oscillations”

Closure to “Steinman on Bridge Oscillations”

Aerodynamic Theory of Bridge Oscillations

General equations are derived, expressing the aerodynamic forces of lift and torque on any oscillating section of two independent degrees of freedom. The parameters representing the distinctive aer...

Aerodynamic Oscillations in Suspension Bridges

Abstract Following the failure in 1940 of the Tacoma Narrows suspension bridge by wind-driven oscillations, the need for developing in advance adequate data concerning wind speeds at which such oscillations occur became apparent. Numerous studies and experiments were undertaken on the subject, the present paper dealing with a symmetrical suspension bridge having two towers in which both sidespan and tower effects are considered. A modification is given to include the effects of roadbed “slats,” and a method is outlined for obtaining flutter speeds from roadbed section models which may fit into standard wind tunnels. The theory is applied to the Tacoma Narrows Bridge.

Oscillations of Suspension Bridges

Abstract The author has developed a theory of oscillations of stiffened cable systems which is applicable to the design of suspension bridges. Dealing with free oscillations in the first part of the paper the author established a system of linear differential equations with variable coefficients taking into account the horizontal displacements and inertia forces, the change of thrust along the cable, the slope of the cable, and the torsional stiffness of the girder. An approximate integration by the Rayleigh energy method is shown and is numerically exemplified for the lowest antisymmetric mode. The results show that, in general, it is allowed to neglect horizontal displacements, change of thrust, and cable sag for the dynamic problem as well as for the static problem and they bring out the fact that for all practical proportions of relative cable sag and girder stiffness the frequencies and modes are essentially independent of the relative cable sag and dead load and only dependent upon the absolute cable sag h so that, for instance, for the lowest antisymmetric mode the equivalent pendulum length is 2h/π2. The second part of the paper treating self-excited oscillations has been prepared under the influence of observations, experiments, and conclusions reached in connection with an (official) report on the Tacoma bridge failure. This report demonstrated that the aerodynamic and structural damping—the first acting through the width of the roadway, the second by the internal friction—plays an important part in the safety of a suspension bridge. It showed further that the dangerous oscillations are of somewhat higher frequency than the free oscillations with logarithmic decrement a linear function of the reduced velocity so that not elastic instability under wind forces nor resonance from wind gusts but the bridge as a self-exciting mechanism absorbing energy out of a steady wind flow had to be assumed as the cause of the failure. This experimental linear decrement law is utilized by the author to derive in conjunction with the dynamic equations formulas intended to serve as the basis for the dynamic requirements for suspension bridges.

Tacoma bridge oscillations being studied by model : Engineering News Record, Vol. 125, No. 5

Tacoma bridge oscillations being studied by model : Engineering News Record, Vol. 125, No. 5

Synchronized Oscillations in Hydrogen Bridges

MOST of the compounds now known to contain intramolecular hydrogen bridges can be represented1 by the formulae: in which X and Y denote oxygen or nitrogen atoms. As indicated, there is undoubtedly resonance between the two extreme structures represented. An equally important but apparently hitherto overlooked stabilizing factor is the tendency of the electron distribution around the ring to shift in synchronism with the oscillational motion of the bridge hydrogen. The electron shifts produced by motion of this hydrogen in the direction X—Y decrease the X—H attraction and increase the Y—H attraction. As a result, the small energy hump which would probably otherwise exist2 in the centre of the bridge is greatly reduced or eliminated entirely, and the bridge stability is increased.