Mechanical resonance is the tendency of a

mechanical system A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to na ...

to respond at greater amplitude when the

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

of its oscillations matches the system's natural frequency of

vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic function, periodic, such as the motion of a pendulum ...

(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, buildings and airplanes. This is a phenomenon known as resonance disaster. Avoiding resonance disasters is a major concern in every building, tower and bridge

construction Construction is a general term meaning the art and science to form objects, systems, or organizations,"Construction" def. 1.a. 1.b. and 1.c. ''Oxford English Dictionary'' Second Edition on CD-ROM (v. 4.0) Oxford University Press 2009 and com ...

project. The

Taipei 101 Taipei 101 (; stylized as TAIPEI 101), formerly known as the Taipei World Financial Center, is a supertall skyscraper in Taipei, Taiwan. This building was officially classified as the world's tallest from its opening in 2004 until the 2009 ...

building relies on a 660-ton

pendulum A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the ...

—a

tuned mass damper A tuned mass damper (TMD), also known as a harmonic absorber or seismic damper, is a device mounted in structures to reduce mechanical vibrations, consisting of a mass mounted on one or more damped springs. Its oscillation frequency is tuned ...

—to modify the response at 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,

engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the l ...

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. It will vibrate easily at those frequencies, and less so at other frequencies. Many

clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the ...

s keep time by mechanical resonance in a balance wheel,

, or quartz crystal.

Description

The natural frequency of a simple mechanical system consisting of a weight suspended by a spring is: :

f =  \sqrt

where ''m'' is the

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

and ''k'' is the spring constant. A swing set is a simple example of a resonant system with which most people have practical experience. It is a form of pendulum. 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: :

f =  \sqrt

where ''g'' is the acceleration due to gravity (about 9.8 m/s² near the surface of

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

), and ''L'' is the length from the pivot point to the center of mass. (An elliptic integral yields a description for any displacement). Note that, in this approximation, the frequency does not depend on

. Mechanical resonators work by transferring energy repeatedly from

kinetic Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory of gases, Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to i ...

to potential form and back again. In the pendulum, for example, all the energy is stored as

gravitational In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...

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 Bob, BOB, or B.O.B. may refer to: Places *Mount Bob, New York, United States *Bob Island, Palmer Archipelago, Antarctica People, fictional characters, and named animals *Bob (given name), a list of people and fictional characters *Bob (surname) ...

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

subharmonic In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must ...

Examples

Various examples of mechanical resonance include: * Musical instruments (

acoustic resonance Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration (its ''resonance frequencies''). The term "acoustic resonance" is sometimes used to nar ...

). *Most

s keep time by mechanical resonance in a balance wheel,

, or quartz crystal. *

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. Then an incident tidal wave can be reinforced b ...

of the

Bay of Fundy The Bay of Fundy (french: Baie de Fundy) is a bay between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine. It is an arm of the Gulf of Maine. Its extremely high tidal range is the hi ...

. * Orbital resonance as in some

moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

s of the

Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...

gas giants A gas giant is a giant planet composed mainly of hydrogen and helium. Gas giants are also called failed stars because they contain the same basic elements as a star. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant ...

. *The resonance of the basilar membrane in the ear. *A wineglass breaking when someone sings a loud note at exactly the right pitch. Resonance may cause violent swaying motions in 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

Broughton Suspension Bridge Broughton Suspension Bridge was an iron chain suspension bridge built in 1826 to span the River Irwell between Broughton and Pendleton, now in Salford, Greater Manchester, England. One of Europe's first suspension bridges, it has been attrib ...

and

Angers Bridge Angers Bridge, also called the Basse-Chaîne Bridge, was a suspension bridge over the Maine (river), Maine River in Angers, France. It was designed by Joseph Chaley and Bordillon, and built between 1836 and 1839.Peters, Tom F., ''"Transitions in ...

). Mechanical systems store potential energy in different forms. For example, a

spring Spring(s) may refer to: Common uses * Spring (season), a season of the year * Spring (device), a mechanical device that stores energy * Spring (hydrology), a natural source of water * Spring (mathematics), a geometric surface in the shape of a ...

/mass system stores energy as tension in the spring, which is ultimately stored as the energy of bonds between

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

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

resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...

frequency, which causes it to

oscillate Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

. Periodic excitation optimally transfers to the

system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...

the

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

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.

Tacoma Narrows Bridge

The dramatic, rhythmic twisting that resulted in the 1940 collapse of "Galloping Gertie", the original

Tacoma Narrows Bridge The Tacoma Narrows Bridge is a pair of twin suspension bridges that span the Tacoma Narrows strait of Puget Sound in Pierce County, Washington. The bridges connect the city of Tacoma with the Kitsap Peninsula and carry State Route 16 (known ...

, is sometimes characterized in physics textbooks as a classic example of resonance. The catastrophic vibrations that destroyed the bridge were due to an oscillation caused by interactions between the bridge and the winds passing through its structure—a phenomenon known as aeroelastic flutter. Robert H. Scanlan, father of the field of bridge aerodynamics, wrote an article about this.

Other examples

* Collapse of

(due to soldiers walking in step) * Collapse of

* Collapse of Königs Wusterhausen Central Tower * Resonance of the

Millennium Bridge Several bridges are known as the Millennium Bridge: * in the United Kingdom **Gateshead Millennium Bridge ** Lune Millennium Bridge, Lancaster ** Millennium Bridge, Glasgow ** Millennium Bridge, London ** Millennium Bridge (Salford Quays) ** Teesqua ...

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 The United States Patent and Trademark Office (USPTO) is an agency in the U.S. Department of Commerce that serves as the national patent office and trademark registration authority for the United States. The USPTO's headquarters are in Alexa ...

classifies devices that tests mechanical resonance under subclass 579,

, or

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...

study, of Class 73,

Measuring Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared t ...

and

test Test(s), testing, or TEST may refer to: * Test (assessment), an educational assessment intended to measure the respondents' knowledge or other abilities Arts and entertainment * ''Test'' (2013 film), an American film * ''Test'' (2014 film), ...

ing. This subclass is itself indented under subclass 570, Vibration.USPTO
Class 73, Measuring and testing
Such devices test an article or

mechanism Mechanism may refer to: *Mechanism (engineering), rigid bodies connected by joints in order to accomplish a desired force and/or motion transmission *Mechanism (biology), explaining how a feature is created *Mechanism (philosophy), a theory that a ...

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 right methods to cause vibrations at a natural mechanical resonance and measure the

and/or

the resonance made. Various devices study the amplitude response over a frequency range is made. This includes

nodal point In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' ...

s, wave lengths, and

standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect ...

characteristics measured under predetermined vibration conditions.

Notes

Patents

* Method and apparatus for inspecting materials * Apparatus for testing textiles * Apparatus for testing textiles and like materials * Testing and adjusting device * Method and apparatus for testing materials * Article testing machine * Apparatus for determining the behavior of suspended cables * Mechanical resonance detection systems * Vibrating-blade relays with electro-mechanical resonance * Quantum mechanical resonance devices * Mechanical resonance indicator * Piezoelectric resonance device * Tuned ground motion detector utilizing principles of mechanical resonance * Apparatus and method for generating mechanical waves * Method of controlling mechanical resonance hand * Apparatus and method for suppressing mechanical resonance in a mass transit vehicle {{authority control Mechanical vibrations Earthquake engineering Resonance ru:Резонанс#.D0.9C.D0.B5.D1.85.D0.B0.D0.BD.D0.B8.D0.BA.D0.B0 sv:Självsvängning