User:Mic shep/Structural acoustics

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 acoustic study, including noise, 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.


 * $$ { \partial^2 w \over  \partial x ^2 }   =  {1 \over c_L^2} { \partial^2 w  \over  \partial t ^2 } $$

where $$w$$ is the deformation $$c_L$$ is the 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 $$\rho$$) of the structure according to


 * $$ { c_L }  =  { \sqrt { B \over \rho } } $$

When two dimensions of the structure are small with respect to wavelength (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 shear deformation occurring in the transverse direction, perpendicular to the wave motion.


 * $$ { \partial^2 w \over  \partial x ^2 }   =  {1 \over c_s^2} { \partial^2 w  \over  \partial t ^2 }  $$

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.

and is slower than compressional waves

Bending Waves (beams, plates, cylinders)
Modes of vibration

Mobility and Impedance

Finite-element Modeling

==Sound-Structure interaction == Fluid structure interaction

Piston radiation

Structural wave radiation

FE/BE Modeling