COMSOL 6.4 - Glossary of Terms

One over the compressibility βs measured at constant entropy. The adiabatic bulk modulus is denoted Ks and gives a measure of the compressibility of the fluid and is directly related to the speed of sound cs in the fluid. SI unit: Pa.

The reciprocal of impedance.

The scientific field of study used to couple acoustics and fluid dynamics.

Variation of material properties with direction.

A technique to formulate equations in a mixed kinematical description. An ALE referential coordinate system is typically a mix between the material (Lagrangian) and spatial (Eulerian) coordinate systems.

An integrated form of Euler’s momentum equation along a line of flow. The equation gives an expression for an invariant quantity in an inviscid fluid. A decrease in the speed of the fluid translates to an increase in the fluid pressure and/or potential energy.

One over the compressibility. It gives a measure of the compressibility of the fluid and is related to the speed of sound in the fluid. SI unit: Pa. See also adiabatic bulk modulus.

The product of the equilibrium density and the speed of sound in a medium. SI unit: Pa/(m/s).

Reciprocal of stiffness.

The inverse of the elasticity matrix. See elasticity matrix.

The most fundamental stress measure defined as force/deformed area in fixed directions not following the body.

Equations that relate two physical quantities. In thermoviscous acoustics both the stress tensor (relating velocity to stress) and Fourier’s law of heat conduction (relating heat conduction to temperature) are constitutive relations. In structural mechanics this is the equation formulating the stress-strain relationship of a material. Constitutive equations are supplemented by equilibrium equations (mass, momentum, and energy) and an equation of state to provide a full physical description.

Time-dependent material nonlinearity that usually occurs in metals at high temperatures in which the effect of the variation of stress and strain with time is of interest.

Dissipation of energy in the fluid or a vibrating structure. The damping is typically due to viscous losses or thermal conduction. In acoustics this happens in structures with small geometrical dimensions, for example, small pipes or porous materials. In structures a common assumption is viscous damping where the damping is proportional to the velocity. See also Rayleigh damping.

Logarithmic unit that indicates the ratio of a physical quantity relative to a reference value.

An acoustic source that behaves as a translational oscillating sphere.

Change in the observed frequency of a wave caused by a time rate of change in the effective length of the path of travel between the source and the observation point.

RMS instantaneous sound pressure at a point during a time interval, T, long enough that the measured value is effectively independent of small changes in T. SI unit: Pa = N/m2.

The thermodynamic relation between three independent thermodynamic variables. Typically in acoustics it is the density ρ = ρ(p,s) given as function of the entropy s and the pressure p.

A possible propagating mode of an acoustic wave.

The matrix D relating strain to stresses:

Model described and solved in a coordinate system that is fixed (spatial). See also Lagrangian and arbitrary Lagrangian–Eulerian method.

Nonlinear strain measure used in large-deformation analysis. In a small strain, large rotation analysis, the Green–Lagrange strain corresponds to the engineering strain, with the strain values interpreted in the original directions. The Green–Lagrange strain is a natural choice when formulating a problem in the undeformed state. The conjugate stress is the second Piola–Kirchhoff stress.

At a specified frequency, the quotient of a dynamic field quantity (such as force, sound, or pressure) by a kinematic field quantity (such as vibration velocity or particle velocity).

Total instantaneous pressure at a point in a medium minus the static pressure at the same point. SI unit: Pa = N/m2.

A velocity field u that has the property of having rotation ∇ × u = 0 everywhere, where the first term is the vorticity of the fluid. In such a fluid the viscous stress does not contribute to the acceleration of the fluid. The mean pressure in this fluid is described by Bernoulli’s equation.

Model described and solved in a coordinate system that moves with the material. See also Eulerian and arbitrary Lagrangian–Eulerian method.

An acoustic source that behaves as a radially oscillating sphere.

In a sound field, the velocity caused by a sound wave of a given infinitesimal part of the medium relative to the medium as a whole.

Domain adjoined at a system boundary designed to emulate a nonreflecting boundary condition independently of the shape and frequency of the incident wavefront.

States that the variation in internal strain energy is equal to the work done by external forces.

The acoustic modes or wave shapes that propagate with no significant damping for a given frequency in a duct of a given cross-section.

A viscous damping model where the damping is proportional to the mass and stiffness through the mass and stiffness damping parameters.

See definition in the entry for sound pressure level.

A frequency at which the system has the tendency to oscillate at a greater amplitude than at nonresonance frequencies. At the resonance frequencies the system can easily transfer energy from the actuation to the vibrating structure or acoustic wave.

Root-mean-square value; for the (complex) sound pressure, p(t), over the time interval T1 < t < T2 defined as

For a harmonic pressure wave,

, the time interval is taken to be a complete period, resulting in pRMS = p0 /√2.

Conjugate stress to Green–Lagrange strain used in large deformation analysis.

Total energy in a given part of a medium minus the energy that would exist at the same part in the absence of sound waves. SI unit: J.

See sound intensity.

Average rate of sound energy transmitted in a specified direction at a point through a unit area normal to this direction. SI unit: W/m2.

See effective sound pressure.

Absolute instantaneous sound pressure in any given cycle of a sound wave at some specified time. SI unit: W/m2.

See sound intensity.

Ten times the logarithm (to the base ten) of the ratio of the time-mean-square pressure of a sound, in a stated frequency band, to the square of a reference sound pressure, pref. For gases, pref = 20 μ Pa, for other media (unless otherwise specified) pref = 1 μ Pa. Unit: dB (decibel).

Maximum instantaneous rate of volume displacement produced by a source when emitting a harmonic sound wave. SI unit: m3/s.

At a point in a sound field, the quotient of sound pressure by particle velocity. SI unit: Pa/(m/s).

The rate of change of particle displacement with distance for a sound wave. SI unit: m/s.

The skew-symmetric part of the velocity gradient tensor.

Pressure that would exist at a point in the absence of a sound wave.

Ratio of change of force (or torque) to the corresponding change in translational (or rotational) displacement of an elastic element.

The interaction between thermodynamic and acoustic phenomena, which takes into account the temperature oscillations that accompany the acoustic pressure oscillations. The combination of these oscillations produces thermoviscous acoustic effects. Thermoviscous acoustic phenomena are modeled by solving the full linearized Navier–Stokes equation (momentum equation), the continuity equation, and the energy equation. Thermoviscous acoustics is also known as viscothermal acoustics or thermoacoustics.

When a flow is irrotational ∇ × u = 0 the vector field (velocity field) can always be derived from a scalar potential ϕ(x) as u = ∇ϕ, where ϕ is the velocity potential. See also irrotational background velocity field.