Structural acoustics is the study of the mechanical

waves United States Naval Reserve (Women's Reserve), better known as the WAVES (for Women Accepted for Volunteer Emergency Service), was the women's branch of the United States Naval Reserve during World War II. It was established on July 21, 1942, ...

in structures 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 acoustician ...

including

noise Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrat ...

, transduction, underwater acoustics, and physical acoustics.

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

B

and

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

\rho

) of the structure according to :

=

When two dimensions of the structure are small with respect to

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

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

Young's modulus Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Youn ...

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

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

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 and the Boundary element method.

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