Mechanical resonance is the tendency of a

mechanical system A machine is a physical system that uses power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolec ...

to respond at greater amplitude when the

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

of its oscillations matches the system's natural frequency of

vibration Vibration () is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the os ...

(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 are processes involved in delivering buildings, infrastructure, industrial facilities, and associated activities through to the end of their life. It typically starts with planning, financing, and design that continues until the a ...

project. The

Taipei 101 The Taipei 101 (; stylized in all caps), formerly known as the Taipei World Financial Center, is a 508 m (1,667 ft), 101-story skyscraper in Taipei, Taiwan. It is owned by Taipei Financial Center Corporation. It was Council on Tall Buildings ...

building for instance relies on a 660-ton

pendulum A pendulum is a device made of 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 i ...

—a tuned mass damper—to modify the response at resonance. The structure is also 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.

Engineer Engineers, as practitioners of engineering, are professionals who Invention, invent, design, build, maintain and test machines, complex systems, structures, gadgets and materials. They aim to fulfill functional objectives and requirements while ...

s designing objects that have 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. Such objects will vibrate easily at those frequencies, and less so at other frequencies. Many

clock A clock or chronometer is a device that measures and displays time. The clock is one of the oldest Invention, human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month, a ...

s keep time by mechanical resonance in a balance wheel,

, or quartz crystal.

Description

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

f =  \sqrt

where ''m'' is the

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

and ''k'' is the

spring constant In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that ...

. For a given mass, stiffening the system (increasing

k

) increases its natural frequency, which is a general characteristic of vibrating mechanical systems. A swing set is another 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 Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

), and ''L'' is the length from the pivot point to the center of mass. (An

elliptic integral In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (). Their name originates from their originally arising i ...

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 to

potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...

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 subharmonics, such as pushing the swing every second or third oscillation.

Examples

Various examples of mechanical resonance include: * Musical instruments ( acoustic resonance). *Most

s keep time by mechanical resonance in a balance wheel,

, or quartz crystal. * Tidal resonance of the

Bay of Fundy The Bay of 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 tidal range is the highest in the world. The bay was ...

. *

Orbital resonance In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relation ...

, as in some

moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

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 "Sola ...

giant planet A giant planet, sometimes referred to as a jovian planet (''Jove'' being another name for the Roman god Jupiter (mythology), Jupiter), is a diverse type of planet much larger than Earth. Giant planets are usually primarily composed of low-boiling ...

s. *The resonance of the

basilar membrane The basilar membrane is a stiff structural element within the cochlea of the inner ear which separates two liquid-filled tubes that run along the coil of the cochlea, the scala media and the scala tympani. The basilar membrane moves up and down ...

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 and Angers Bridge). Mechanical systems store potential energy in different forms. For example, a spring/mass system stores energy as tension in the spring, which is ultimately stored as the energy of bonds between

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

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 resonant 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 pendulu ...

. Periodic excitation optimally transfers to the

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

the

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

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 bridges, twin suspension bridges that span the Tacoma Narrows strait of Puget Sound in Pierce County, Washington, Pierce County, Washington (state), Washington. The bridges connect the city of Tacom ...

, 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 Broughton Suspension Bridge (due to soldiers walking in step) * Collapse of Angers Bridge * Collapse of Königs Wusterhausen Central Tower * Resonance of the Millennium Bridge

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 Ale ...

classifies devices that tests mechanical resonance under subclass 579,

resonance Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

, 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 am ...

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 to ...

and testing. 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 (economics), a set of rules for a game designed to achieve a certain outcome **Mechanism design, the study of such mechanisms *Mechanism (engineering), rigid bodies connected by joints in order to accomplish 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 Spectral bands are regions of a given spectrum, having a specific range of wavelengths or frequencies. Most often, it refers to electromagnetic bands, regions of the electromagnetic spectrum. More generally, spectral bands may also be means in ...

is made. This includes nodal points, 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 t ...

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