Quantities¶

The following is a list of all physical quantities relevant to SEA.

General quantities¶

frequency: Frequency f is the number of occurrences of a repeating event per unit time and has the unit hertz (Hz).
angular frequency: Angular frequency $\omega$ is the frequency of an oscillation in unit radians per second (rad/s).

$\omega = 2 \pi f$
speed of sound: Speed of sound c describes the speed at which a wave passes through a medium.

Phase speed $c_{phase}$

Group speed $c_{group}$

aera moment of inertia second moment of inertia: Area moment of area, also known as ‘second moment of inertia, ‘moment of inertia of plane area, or ‘second area moment’, is a geometrical property of an area which reflects how its points are distributed with regards to an arbitrary axis. It has unit (m^4).
torsional moment of rigidity: The torsional moment of rigidity J
radius of gyration: Radius of gyration $\kappa$ or gyradius is the name of several related measures of the size of an object, a surface, or an ensemble of points. It is calculated as the root mean square distance of the objects’ parts from either its center of gravity or a given axis.

See also

http://en.wikipedia.org/wiki/Radius_of_gyration

velocity

The velocity v

velocity level

The velocity level $L_v$ is given by

$L_v = 20 \log_{10}{\frac{v}{v_0}}$

where $v_0$ is a reference velocity.

mobility

The mobility Y describes how easily a body moves when subject to a force.

energy

The energy E

power dissipation

The power dissipation P in a subsystem i is given by

$P_{dis,i} = \omega \eta n_i$

where $\eta$ is the loss factor of the subsystem.

density: The density $\rho$
young’s modulus: Young’s modulus E, also known as the tensile modulus or elastic modulus, is a measure of the stiffness of an elastic material, and has the unit pascal (Pa).
bending stiffness flexural rigidity: The bending stiffness or flexural rigidity D.
shear modulus: Shear modulus G or modulus of rigidity, is defined as the ratio of shear stress to the shear strain, and has the unit pascal (Pa).
bulk modulus: Bulk modulus K of a substance measures the substance’s resistance to uniform compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume, and has the unit pascal (Pa).
poisson’s ratio: Poisson’s ratio $\nu$ is the negative ratio of transverse to axial strain. Poisson’s ratio is dimensionless.
loss factor: Loss factor $\eta$ describes the amount of energy lost per cycle.

$\eta = \frac{W}{E \omega}$