Structural acoustics is the study of the mechanical

waves Waves most often refers to: * Waves, oscillations accompanied by a transfer of energy that travel through space or mass. * Wind waves, surface waves that occur on the free surface of bodies of water. Waves may also refer to: Music *Waves (ban ...

structures A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...

and how they interact with and radiate into adjacent media. The field of structural acoustics is often referred to as vibroacoustics in Europe and Asia. People that work in the field of structural acoustics are known as structural acousticians. The field of structural acoustics can be closely related to a number of other fields of

acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acousticia ...

including

noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...

, transduction,

underwater acoustics Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Ty ...

, and

physical acoustics Physical acoustics is the area of acoustics and physics that studies interactions of acoustic waves with a gaseous, liquid or solid medium on macro- and micro-levels. This relates to the interaction of sound with thermal waves in crystals (phonons) ...

Vibrations in structures

Compressional and shear waves (isotropic, homogeneous material)

Compressional waves (often referred to as longitudinal waves) expand and contract in the same direction (or opposite) as the wave motion. The wave equation dictates the motion of the wave in the x direction. :

=

where

u

is the displacement and

c_L

is the longitudinal wave speed. This has the same form as the acoustic wave equation in one-dimension.

c_L

is determined by properties (

bulk modulus The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other moduli descri ...

B

and

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...

\rho

) of the structure according to :

=

When two dimensions of the structure are small with respect to

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...

(commonly called a beam), the wave speed is dictated by Youngs modulus

E

instead of the

B

and are consequently slower than in infinite media. Shear waves occur due to the shear stiffness and follows a similar equation, but with the displacement occurring in the transverse direction, perpendicular to the wave motion. :

=

The shear wave speed is governed by the

shear modulus In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackre ...

G

which is less than

E

and

B

, making shear waves slower than longitudinal waves.

Bending waves in beams and plates

Most sound radiation is caused by bending (or flexural) waves, that deform the structure transversely as they propagate. Bending waves are more complicated than compressional or shear waves and depend on material properties as well as geometric properties. They are also dispersive since different frequencies travel at different speeds.

Modeling vibrations

Finite element analysis The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

can be used to predict the vibration of complex structures. A finite element computer program will assemble the mass, stiffness, and damping matrices based on the element geometries and material properties, and solve for the vibration response based on the loads applied. :

Sound-structure interaction

Fluid-structure Interaction

When a vibrating structure is in contact with a fluid, the normal particle velocities at the interface must be conserved (i.e. be equivalent). This causes some of the energy from the structure to escape into the fluid, some of which radiates away as sound, some of which stays near the structure and does not radiate away. For most engineering applications, the numerical simulation of fluid-structure interactions involved in vibro-acoustics may be achieved by coupling the

Finite element method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

and the

Boundary element method The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, el ...

References

External links

asa.aip.org
{{Webarchive, url=https://web.archive.org/web/19961119081746/http://asa.aip.org/ , date=1996-11-19 —Website of the

Acoustical Society of America The Acoustical Society of America (ASA) is an international scientific society founded in 1929 dedicated to generating, disseminating and promoting the knowledge of acoustics and its practical applications. The Society is primarily a voluntary org ...

Acoustics Sound