Mechanical resonance is the tendency of a
mechanical systemMechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment....
to absorb more energy when the
frequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
of its oscillations matches the system's natural frequency of
vibrationVibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...
(its
resonance frequency or
resonant frequency) than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, and airplanes a phenomenon known as resonance disaster.
Avoiding resonance disasters is a major concern in every building, tower and bridge
constructionIn the fields of architecture and civil engineering, construction is a process that consists of the building or assembling of infrastructure. Far from being a single activity, large scale construction is a feat of multitasking...
project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The
Taipei 101Taipei 101 , also known as the Taipei Financial Center, is a landmark skyscraper located in Xinyi District, Taipei, Taiwan. The building, designed by C.Y...
building relies on a 660-ton
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
— a
tuned mass damperA tuned mass damper, also known as an active mass damper or harmonic absorber, is a device mounted in structures to prevent discomfort, damage, or outright structural failure caused by vibration...
— to cancel resonance. Furthermore, the structure is designed to resonate at a frequency which does not typically occur. Buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. In addition,
EngineerEngineers are concerned with developing economical and safe solutions to practical problems, by applying mathematics and scientific knowledge while considering technical constraints. The term is derived from the Latin root "ingenium," meaning "cleverness"...
s designing objects having engines must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other strongly oscillating parts.
Many resonant objects have more than one resonance frequency, particularly at
harmonicIn acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is...
s (multiples) of the strongest resonance. It will vibrate easily at those frequencies, and less so at other frequencies. Many
clockA clock is an instrument used to indicate, measure, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell"...
s keep time by mechanical resonance in a
balance wheelThe balance wheel is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral spring, the balance spring or hairspring...
,
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
, or
quartz crystalA quartz clock is a clock that uses an electronic oscillator that is regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks are at least an order of magnitude more accurate than good mechanical clocks...
Description
The resonance frequency of a simple mechanical system consisting of a weight suspended by a spring is:
where
M is the
massIn physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass...
and
k is the spring constant.
A
swing setSwing Set is an EP by Ani Difranco, released July 11, 2000 on Righteous Babe Records.-Track listing:#"Swing " – 3:57#"Swing " – 6:13#"To the Teeth " – 6:12...
is a simple example of a resonant system with which most people have practical experience. It is a form of
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
. If the system is excited (pushed) with a period between pushes equal to the inverse of the pendulum's natural frequency, the swing will swing higher and higher, but if excited at a different frequency, it will be difficult to move. The resonance frequency of a pendulum, the only frequency at which it will vibrate, is given approximately, for small displacements, by the equation:
where
g is the
acceleration due to gravityStandard gravity, usually denoted by g0 or gn, is the nominal acceleration due to gravity at the Earth's surface at sea level, defined to be precisely 9.80665 m/s2 . This value was established by the 3rd CGPM...
(about 9.8 m/s
2 near the surface of
EarthEarth is the third planet from the Sun. It is the fifth largest of the eight planets in the solar system, and the largest of the terrestrial planets in the Solar System in terms of diameter, mass and density...
), and
L is the length from the pivot point to the center of mass. (An
elliptic integralIn integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse. They were first studied by Giulio Fagnano and Leonhard Euler...
yields a description for any displacement.) Note that, in this approximation, the frequency does not depend on
massIn physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass...
.
Mechanical resonators work by transferring energy repeatedly from
kineticThe kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its...
to
potentialPotential energy is energy stored within a physical system as a result of the position or configuration of the different parts of that system. It is called potential energy because it has the potential to be converted into other forms of energy, such as kinetic energy, and to do work in the process...
form and back again. In the pendulum, for example, all the energy is stored as gravitational energy (a form of potential energy) when the bob is instantaneously motionless at the top of its swing. This energy is proportional to both the mass of the bob and its height above the lowest point. As the bob descends and picks up speed, its potential energy is gradually converted to kinetic energy (energy of movement), which is proportional to the bob's mass and to the square of its speed. When the bob is at the bottom of its travel, it has maximum kinetic energy and minimum potential energy. The same process then happens in reverse as the bob climbs towards the top of its swing.
Some resonant objects have more than one resonance frequency, particularly at harmonics (multiples) of the strongest resonance. It will vibrate easily at those frequencies, and less so at other frequencies. It will "pick out" its resonance frequency from a complex excitation, such as an impulse or a wideband noise excitation. In effect, it is filtering out all frequencies other than its resonance. In the example above, the swing cannot easily be excited by harmonic frequencies, but can be excited by
subharmonicSubharmonic frequencies are frequencies below the fundamental frequency of an oscillator in a ratio of . For example, if the fundamental frequency of an oscillator is 440 Hz, sub-harmonics include 220 Hz and 110 Hz . Thus, they are a mirror image of the harmonic series.Subharmonics can be produced...
s.
Examples
Various examples of mechanical resonance include:
- musical instruments (acoustic resonance
Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own natural frequencies of vibration than it does at other frequencies...
).
- Most clock
A clock is an instrument used to indicate, measure, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell"...
s keep time by mechanical resonance in a balance wheelThe balance wheel is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral spring, the balance spring or hairspring...
, pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
, or quartz crystalA quartz clock is a clock that uses an electronic oscillator that is regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks are at least an order of magnitude more accurate than good mechanical clocks...
.
- tidal resonance
In oceanography, a tidal resonance occurs when the tide excites one of the resonant modes of the ocean. The effect is most striking when a continental shelf is about a quarter wavelength wide...
of the Bay of FundyThe Bay of Fundy is a bay on the Atlantic coast of North America, on the northeast end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine...
.
- Orbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
as in some moonA natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called the primary. Technically, the term natural satellite could refer to a planet orbiting a star, or a dwarf galaxy orbiting a major galaxy, but it is normally synonymous with moon and used to identify...
s of the solar systemThe Solar System consists of the Sun and those celestial objects bound to it by gravity, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago...
's gas giantsGas Giants were a pop rock band from Tempe, Arizona, formed as a successor project to the Gin Blossoms. The group was known as The Pharaohs when they formed in 1997, but changed their name after their label, A&M Records, merged with Universal Records and the band changed hands, re-signing with...
.
- The resonance of the basilar membrane
The basilar membrane within the cochlea of the inner ear is a stiff structural element that separates two liquid-filled tubes that run along the coil of the cochlea, the scala media and the scala tympani .-Function:...
in the earThe ear is the organ that detects sound. The vertebrate ear shows a common biology from fish to humans, with variations in structure according to order and species. It not only acts as a receiver for sound, but plays a major role in the sense of balance and body position...
.
- Making a child's swing
A swing is a hanging seat, usually found in a playground for children, a circus for acrobats, or on a porch for relaxing. The seat of a swing can be attached to a chain or a rope...
swing higher by pushing it at each swing.
- A wineglass breaking when someone sings a loud note at exactly the right pitch.
Resonance may cause violent swaying motions in improperly constructed structures, such as bridges and buildings. The London Millennium Footbridge (nicknamed the
Wobbly Bridge) exhibited this problem. A faulty bridge can even be destroyed by its resonance (see "
Angers BridgeAngers Bridge, also called the Basse-Chaîne Bridge, was a suspension bridge over the Maine River in Angers, France. It was designed by Joseph Chaley and Bordillon, and built between 1836 and 1839. The bridge collapsed on April 16, 1850, when 478 French soldiers marched across it in lockstep.The...
"; that is why soldiers are trained not to march in lockstep across a bridge, although it is suspected to be a myth, see eg.,
MythBusters (season 2)The cast of the television series MythBusters perform experiments to verify or debunk urban legends, old wives' tales, and the like. This is a list of the various myths tested on the show as well as the results of the experiments .The myths the show has tested for accuracy in Season 2 include:-...
. Mechanical systems store potential energy in different forms. For example, a
springA spring is an elastic object used to store mechanical energy. Springs are usually made out of hardened steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...
/mass system stores energy as tension in the spring, which is ultimately stored as the energy of bonds between
atomThe atom is a basic unit of matter consisting of a dense, central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s.
Resonance disaster
In mechanics and construction a
resonance disaster describes the destruction of a building or a technical mechanism by induced vibrations at a system's
resonanceIn physics, resonance is the tendency of a system to oscillate at larger amplitude at some frequencies than at others. These are known as the system's resonant frequencies . At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system...
frequency, which causes it to oscillate. Periodic exitation optimally transfers to the
systemSystem is a set of interacting or interdependent entities forming an integrated whole....
the
energyIn physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law...
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. As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The
Taipei 101Taipei 101 , also known as the Taipei Financial Center, is a landmark skyscraper located in Xinyi District, Taipei, Taiwan. The building, designed by C.Y...
building relies on a 660-ton
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
— a
tuned mass damperA tuned mass damper, also known as an active mass damper or harmonic absorber, is a device mounted in structures to prevent discomfort, damage, or outright structural failure caused by vibration...
— to cancel resonance. Furthermore, the structure is designed to resonate at a frequency which does not typically occur. Buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. Avoiding resonance disasters is a major concern in every building, tower and bridge
constructionIn the fields of architecture and civil engineering, construction is a process that consists of the building or assembling of infrastructure. Far from being a single activity, large scale construction is a feat of multitasking...
project.
Failure of the original Tacoma Narrows Bridge
The dramatic, rhythmic twisting that resulted in the 1940 collapse of "Galloping Gertie," the original
Tacoma Narrows BridgeThe original Tacoma Narrows Bridge opened on July 1, 1940, and dramatically collapsed into Puget Sound on November 7 of the same year. The suspension bridge spanned the Tacoma Narrows strait between Tacoma and the Kitsap Peninsula, in the United States. Its replacement was opened in the same...
, is sometimes characterized in physics textbooks as a classic example of resonance; however, this description is misleading. The catastrophic vibrations that destroyed the bridge were not due to simple mechanical resonance, but to a more complicated oscillation caused by interactions between the bridge and the winds passing through its structure — a phenomenon known as aeroelastic flutter.
Robert H. ScanlanRobert H. Scanlan was a civil and aeronautical engineer who came to be widely recognized as a leader in the analysis of wind effects on large structures. Scanlan created the concept of flutter derivatives to aid in the representation of self-excited forces in theoretical models...
, father of the field of bridge aerodynamics, wrote an article about this misunderstanding.
Other Examples
- Collapse of Angers Bridge
Angers Bridge, also called the Basse-Chaîne Bridge, was a suspension bridge over the Maine River in Angers, France. It was designed by Joseph Chaley and Bordillon, and built between 1836 and 1839. The bridge collapsed on April 16, 1850, when 478 French soldiers marched across it in lockstep.The...
- Collapse of Königs Wusterhausen Central Tower
The Central tower in Königs Wusterhausen was a 243 meter high, free standing steel framework tower on the Funkerberg of Königs Wusterhausen, Germany...
Applications
Various method of inducing mechanical resonance in a medium exist. Mechanical waves can be generated in a medium by subjecting an electromechanical element to an alternating electric field having a frequency which induces mechanical resonance and is below any electrical resonance frequency. Such devices can apply mechanical energy from an external source to an element to mechanically stress the element or apply mechanical energy produced by the element to an external load.
The United States Patent Office classifies devices that tests mechanical resonance under subclass 579,
resonanceIn physics, resonance is the tendency of a system to oscillate at larger amplitude at some frequencies than at others. These are known as the system's resonant frequencies . At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system...
,
frequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
, or
amplitudeAmplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
study, of Class 73, Measuring and
testIn scientific research, an experiment is a method of investigating causal relationships among variables, or to test a hypothesis. An experiment is a cornerstone of the empirical approach to acquiring data about the world and is used in both natural sciences and social sciences...
ing. This subclass is itself indented under subclass 570, Vibration. Such devices test an article or
mechanismMechanism may refer to:*Mechanism , explaining how a feature is created* Mechanism , explaining a reaction pathway*Mechanism , a theory that all natural phenomena can be explained by physical causes...
by subjecting it to a vibratory force for determining qualities, characteristics, or conditions thereof, or sensing, studying or making analysis of the vibrations otherwise generated in or existing in the article or mechanism. Devices include methods to cause vibrations at a natural mechanical resonance and measure the
frequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
and/or
amplitudeAmplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
the resonance made. Various devices study the amplitude response over a
frequency rangeA frequency range or frequency band is a range of wave frequencies. It most often refers to either a range of frequencies in sound or a range of frequencies in electromagnetic radiation, which includes light and radio waves....
is made. This includes nodal points, wave lengths, and
standing waveA standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite...
characteristics measured under predetermined vibration conditions.
Earthquake machine
Nikola TeslaNikola Tesla was an inventor and a mechanical and electrical engineer. He is frequently cited as one of the most important contributors to the birth of commercial electricity and is best known for his many revolutionary developments in the field of electromagnetism in the late 19th and early 20th...
established a laboratory on Houston Street in New York at 46 E. There, at one point while experimenting with mechanical oscillators, he allegedly generated a resonance of several buildings causing complaints to the police. As the speed grew he hit the resonance frequency of his own building and belatedly realizing the danger he was forced to apply a sledge hammer to terminate the experiment, just as the astonished police arrived. The Discovery Channel's popular
MythBustersMythBusters is a popular science television program produced by Australian company Beyond Television Productions originally for the Discovery Channel in the United States. The series has since been distributed by a number of international broadcasters, including SBS in Australia and BBC2 in the UK...
show examined Tesla's claim that he had created an "Earthquake Machine" in their 60th episode. They tested the physical phenomenon known as mechanical resonance on a traffic
bridgeA bridge is a structure built to span a valley, road, body of water, or other physical obstacle, for the purpose of providing passage over the obstacle. Designs of bridges vary depending on the function of the bridge and the nature of the terrain where the bridge is constructed.-History:The first...
, which today are built to withstand such forces. While a single I-beam of steel was deflected several feet in each direction by their oscillator, and they reportedly felt the bridge shaking many yards away, there were no "earth shattering" effects. It is worth indicating that, in the time of the event undertaken by Tesla, buildings were not built to withstand such resonance.
See also
Devices:
ResonatorA resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonance frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...
s,
Reed switchThe reed switch is an electrical switch operated by an applied magnetic field. It was invented at Bell Telephone Laboratories in 1936 by W. B. Ellwood. It consists of a pair of contacts on ferrous metal reeds in a hermetically sealed glass envelope...
es,
TransducerA transducer is a device, electrical, electronic, electro-mechanical, electromagnetic, photonic, or photovoltaic, that converts one type of energy or physical attribute to another for various purposes including measurement or information transfer .There are two kinds of transducers...
s
Non-mechanical:
ResonanceIn physics, resonance is the tendency of a system to oscillate at larger amplitude at some frequencies than at others. These are known as the system's resonant frequencies . At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system...
,
Electrical resonanceElectrical resonance occurs in an electric circuit at a particular resonance frequency when the impedance between the input and output of the circuit is at a minimum...
,
Laser applicationsThere are many scientific, military, medical and commercial laser applications which have been developed since the invention of the laser in the 1958...
Other:
VibrationVibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...
s,
Nikola TeslaNikola Tesla was an inventor and a mechanical and electrical engineer. He is frequently cited as one of the most important contributors to the birth of commercial electricity and is best known for his many revolutionary developments in the field of electromagnetism in the late 19th and early 20th...
,
Resonance disaster,
Dunkerley's MethodDunkerley's method is used in mechanical engineering to determine the critical speed of a shaft-rotor system. Other methods include the Rayleigh–Ritz method.-Whirling of a shaft:...
- String resonance, mechanical resonance in string instruments
External links and references
Citations
Publications
- S Spinner, WE Tefft, A method for determining mechanical resonance frequencies and for calculating elastic moduli from these frequencies. American Society for testing and materials.
- CC Jones, A mechanical resonance apparatus for undergraduate laboratories. American Journal of Physics, 1995.
Patents
Websites