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The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient:
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh [1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. [ 2 ] [ 3 ] [ 4 ] It characterises the fluid's flow regime: [ 5 ] a value in a certain lower range denotes laminar flow ; a value in a higher range ...
controls the amount of damping, α {\displaystyle \alpha } controls the linear stiffness , β {\displaystyle \beta } controls the amount of non-linearity in the restoring force; if β = 0 , {\displaystyle \beta =0,} the Duffing equation describes a damped and driven simple harmonic oscillator ,
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
physics, engineering (Damping ratio of oscillator or resonator; energy stored versus energy lost) Relative density: RD = hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)
In applied mathematics, a damping matrix is a matrix corresponding to any of certain systems of linear ordinary differential equations. A damping matrix is defined as follows. If the system has n degrees of freedom u n and is under application of m damping forces .
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom .
In fluid thermodynamics, Rayleigh–Bénard convection is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Bénard cells.