Structural acoustics
Encyclopedia
Structural acoustics is the study of the mechanical waves
in structures and how they interact with and radiate into adjacent fluids. 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
including noise
, transduction
, underwater acoustics
, and physical acoustics.
where
is the deformation 
is the wave speed. This has the same form as the acoustic wave equation
in one-dimension.
is determined by properties (bulk modulus
and density
) of the structure according to
When two dimensions of the structure are small with respect to wavelength
(commonly called a beam), the wave speed is dictated by Youngs modulus
instead of the 
and are consequently slower than in infinite media.
Shear waves occur due to the shear stiffness and follows a similar equation, but with the shear deformation occurring in the transverse direction, perpendicular to the wave motion.
The shear wave speed is governed by the shear modulus
which is less than 
and 
, making shear waves slower than longitudinal waves.
since different frequencies travel as different speeds. For a thin beam then bending wave speed is defined as
and the wave equation is fourth order in space. For a thin plate the bending wave speed is
where
.
where
is the piston velocity (assumed constant over the surface) and 
is the first order Bessel function
. This is derived by integrating the far-field pressure contributions of tiny point sources over the area of the piston. The radiated sound power is related directly to the radiation resistance of the fluid and is calculated as
where
is the spatially and time averaged velocity.
WAVES
The WAVES were a World War II-era division of the U.S. Navy that consisted entirely of women. The name of this group is an acronym for "Women Accepted for Volunteer Emergency Service" ; the word "emergency" implied that the acceptance of women was due to the unusual circumstances of the war and...
in structures and how they interact with and radiate into adjacent fluids. 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
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
including noise
Noise
In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...
, transduction
Transducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...
, underwater acoustics
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 and its boundaries. The water may be in the ocean, a lake or a tank. Typical frequencies associated with underwater acoustics are between 10 Hz and...
, and physical acoustics.
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
is the deformation is the wave speed. This has the same form as the acoustic wave equationAcoustic wave equation
In physics, the acoustic wave equation governs the propagation of acoustic waves through a material medium. The form of the equation is a second order partial differential equation. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position r and...
in one-dimension.
is determined by properties (bulk modulusBulk modulus
The bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to decrease the volume by a factor of 1/e...
and densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
) of the structure according toWhen two dimensions of the structure are small with respect to wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
(commonly called a beam), the wave speed is dictated by Youngs modulus
instead of the and are consequently slower than in infinite media.Shear waves occur due to the shear stiffness and follows a similar equation, but with the shear deformation occurring in the transverse direction, perpendicular to the wave motion.
The shear wave speed is governed by the shear modulus
which is less than and , making shear waves slower than longitudinal waves.Bending Waves in beams and plates
Most sound radiation is caused by bending (or flexural) waves, which 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 dispersiveDispersive
*Dispersive partial differential equation*Dispersive phase from Biological dispersal*Dispersive medium*dispersive line*dispersive mass transfer*dispersive power*dispersive fading...
since different frequencies travel as different speeds. For a thin beam then bending wave speed is defined as
and the wave equation is fourth order in space. For a thin plate the bending wave speed is
where
.Modeling Vibrations
Finite element analysis can be used to predict the vibration of complex structures. A finite element compute 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.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.Piston Radiation
A piston oscillating uniformly in a rigid baffle is the classic example to consider acoustic radiation. For a circular piston that has time harmonic motion, the pressure far away from the piston is found to bewhere
is the piston velocity (assumed constant over the surface) and is the first order Bessel functionBessel function
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...
. This is derived by integrating the far-field pressure contributions of tiny point sources over the area of the piston. The radiated sound power is related directly to the radiation resistance of the fluid and is calculated as
where
is the spatially and time averaged velocity.Structural Wave Radiation
Since most structures do not vibrate uniformly (as in the case of the baffled piston), but vibrate according as combinations of flexural, compressional and shear waves. The radiation characteristics actually depend strongly on whether the bending wave speed is slower than the sound speed in the fluid or faster. For subsonic bending waves, the radiation is weak, while supersonic bending waves radiate efficiently.See also
- AcousticsAcousticsAcoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
- Academic Programs in AcousticsAcademic Programs in AcousticsThis page offers a partial list of academic institutions that offer significant exposure to the science of acoustics. Because acoustics is a broad, multi-disciplinary field, many institutions offer acoustics courses through various other departments, such as physics, architecture, or a particular...
- Acoustic wave equationAcoustic wave equationIn physics, the acoustic wave equation governs the propagation of acoustic waves through a material medium. The form of the equation is a second order partial differential equation. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position r and...
- Lamb wave
- Linear elasticityLinear elasticityLinear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity models materials as continua. Linear elasticity is a simplification of the more general nonlinear theory of elasticity and is a branch of...
- Noise controlNoise controlNoise control is an active or passive means of reducing sound emissions, often incentivised by personal comfort, environmental considerations or legal compliance. Practical and efficient noise control is wholly reliant on an accurate diagnosis of what is causing the noise, which first involves...
- SoundSoundSound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
- Surface acoustic waveSurface acoustic wave]A surface acoustic wave is an acoustic wave traveling along the surface of a material exhibiting elasticity, with an amplitude that typically decays exponentially with depth into the substrate.-Discovery:...
- WavesWAVESThe WAVES were a World War II-era division of the U.S. Navy that consisted entirely of women. The name of this group is an acronym for "Women Accepted for Volunteer Emergency Service" ; the word "emergency" implied that the acceptance of women was due to the unusual circumstances of the war and...
- Wave equationWave equationThe wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...
External links
- arl.psu.edu/structural_acoustics—Website of the Penn State University's Structural Acoustics Group
- asa.aip.org—Website of the Acoustical Society of AmericaAcoustical Society of AmericaThe Acoustical Society of America is an international scientific society dedicated to increasing and diffusing the knowledge of acoustics and its practical applications.-History:...