Resonance is caused by periodic energy transfer at a system's natural frequency.
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Reference materials state that resonance occurs when periodic forces or excitation match a system's natural frequency, allowing energy to be transferred and stored.
The dramatic Tacoma Narrows bridge disaster of 1940 is still very much in the public eye today. Notably, in many undergraduate physics texts the disaster is presented as an example of elementary forced resonance of a mechanical oscillator, with the wind providing an external periodic frequency that matched the natural structural frequency. This oversimplified explanation has existed in numerous texts for a long time and continues to this day, with even more detailed presentation in some new and updated texts. Engineers, on the other hand, have studied the phenomenon over the past half-century, and their current understanding differs fundamentally from the viewpoint expressed in most physics texts. In the present article the engineers’ viewpoint is presented to the physics community to make it clear where substantial disagreement exists. First it is pointed out that one misleading identification of forced resonance arises from the notion that the periodic natural vortex shedding of the wind over the structure was the source of the damaging external excitation. It is then demonstrated that the ultimate failure of the bridge was in fact related to an aerodynamically induced condition of self-excitation or ‘‘negative damping’’ in a torsional degree of freedom. The aeroelastic phenomenon involved was an interactive one in which developed wind forces were strongly linked to structural motion. This paper emphasizes the fact that, physically as well as mathematically, forced resonance and self-excitation are fundamentally different phenomena. The paper closes with a quantitative assessment of the Tacoma Narrows phenomenon that is in full agreement with the documented action of both the bridge itself in its final moments and a full, dynamically scaled model of it studied in the 1950s.
The mechanism and the characteristics of the cable-deck coupled nonlinear vibration in a cable-stayed bridge are studied using numerical methods. A simple three-degrees-of-freedom (d.f.) model, with one independent d.f. for modeling the bridge deck movement, is proposed for describing the nonlinear interactions between the in-plane/out-of-plane vibration of the cable and the oscillation of the bridge deck. The governing equations are discretized with the Galerkin method and then solved with a numerical time integration algorithm. It is pointed out that the periodic variation of cable tension caused by vibration of a bridge deck will lead to the parametric resonance of the stay cable under certain tuning conditions. Numerical results also confirm that energy transfer between different vibration modes and beating phenomenon of the cable-deck vibration may be exhibited in the case of parametric resonance.
larger amplitudes at certain frequencies, known as the system's natural frequencies. At these frequencies, even relatively small periodic driving forces
The 1940 Tacoma Narrows Bridge, the first bridge at this location, was a suspension bridge in the U.S. state of Washington that spanned the Tacoma Narrows strait of Puget Sound between Tacoma and the Kitsap Peninsula. It opened to traffic on July 1, 1940, and dramatically collapsed into Puget Sound on November 7 of the same year. The bridge's collapse has been described as "spectacular" and in sub
The bridge's spectacular destruction is often used as an object lesson in the necessity to consider both aerodynamics and resonance effects in civil and structural engineering. Billah and Scanlan (1991) reported that, in fact, many physics textbooks (for example Resnick et al. and Tipler et al.) wrongly explain that the cause of the failure of the Tacoma Narrows bridge was externally forced mechanical resonance. Resonance is the tendency of a system to oscillate at larger amplitudes at certain frequencies, known as the system's natural frequencies. At these frequencies, even relatively small periodic driving forces can produce large amplitude vibrations, because the system stores energy. For example, a child using a swing realizes that if the pushes are properly timed, the swing can move with a very large amplitude. The driving force, in this case the child pushing the swing, exactly replenishes the energy that the system loses if its frequency equals the natural frequency of the system.
Usually, the approach taken by those physics textbooks is to introduce a first order forced oscillator, defined by the second-order differential equation
resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency
Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) closer than it does other frequencies. It may cause violent swaying motions and potentially catastrophic failure in improperly constructed structures including bridges,
In mechanics and construction a resonance disaster describes the destruction of a building or a technical mechanism by induced vibrations at a system's resonant frequency, which causes it to oscillate. Periodic excitation optimally transfers to the system the energy of the vibration and stores it there. Because of this repeated storage and additional energy input the system swings ever more strongly, until its load limit is exceeded.
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