4.7.3)kigeneralised stiffness with respect to the ith mode, defined as
Kconstant on right hand side of Bernouilli equationKCKeulegan–Carpenter numberKPpower coefficient based on tip speedKSMBsize reduction factor accounting for the lack of correlation of wind fluctuations over structural element or elementsKSx(n1)size reduction factor accounting for the lack of correlation of wind fluctuations at resonant frequency over structural element or elementsKv()modified Bessel function of the second kind and order vK(χ)function determining the induced velocity normal to the plane of a yawed rotorLlength scale for turbulence (subscripts and superscripts according to context); lift force; wave length
integral length scale for the along‐wind turbulence component, u, measured in the longitudinal direction, xmmass per unit length; integer; depth below seabed of effective monopole fixity; inverse slope of log‐log plot of S‐N curvemaadded mass per unit span of blademigeneralised mass with respect to the ith modemT1generalised mass of tower, nacelle, and rotor with respect to tower first modeMmoment; integer; tower top mass; mass of floating structure
mean bending momentMpeak quasi‐static mudline momentM1(t)fluctuating cantilever root bending moment due to excitation of first modeMTteeter momentMXblade in‐plane moment (i.e. moment causing bending in plane of rotation); tower side‐to‐side momentMYblade out‐of‐plane moment (i.e. moment causing bending out‐of‐plane of rotation); tower fore–aft momentMZblade torsional moment; tower torsional momentMYSlow‐speed shaft moment about rotating axis perpendicular to axis of blade 1MZSlow‐speed shaft moment about rotating axis parallel to axis of blade 1MYNmoment exerted by low‐speed shaft on nacelle about (horizontal) y axisMZNmoment exerted by low‐speed shaft on nacelle about (vertical) z axisnfrequency (Hz); number of fatigue loading cycles; integer; distance measured normal to a surfacenzero up‐crossing frequency of quasi‐static responsen1frequency (Hz) of first mode of vibrationNnumber of timesteps per revolution; integer; design fatigue life in number of cycles for a given constant stress rangeN(r)centrifugal forceN(S)number of fatigue cycles to failure at stress level Spstatic pressurep()probability density functionPaerodynamic power; electrical real (active) power
associated Legendre polynomial of the first kindq(r, t)fluctuating aerodynamic lift per unit lengthQrotor torque; electrical reactive powerQaaerodynamic torque
rate of heat flow
mean aerodynamic lift per unit lengthQDdynamic factor defined as ratio of extreme moment to gust quasi‐static momentQgload torque at generatorQLloss torque
associated Legendre polynomial of the second kindQ1(t)generalised load, defined in relation to a cantilever blade by Eq. (A5.13)rradius of blade element or point on blade; correlation coefficient between power and wind speed; radius of tubular tower; radius of monopiler′radius of point on blader1, r2radii of points on blade or bladesRblade tip radius; ratio of minimum to maximum stress in fatigue load cycle; electrical resistanceReReynolds numberRu(n)normalised power spectral density, n.Su(n)/
, of longitudinal wind speed fluctuations, u, at a fixed pointsdistance inboard from the blade tip; distance along the blade chord from the leading edge; separation between two points; Laplace operator; slip of induction machine; spacing of columns of a semi‐submersibles1separation between two points measured in the along‐wind directionSwing area; autogyro disc area; fatigue stress range; surface areaS(apparent) electrical power (bold indicates a complex quantity)S()uncertainty or error bandSjk(n)cross‐spectrum of longitudinal wind speed fluctuations, u, at points j and k (single‐sided)SM(n)single‐sided power spectrum of bending momentSQ1(n)single‐sided power spectrum of generalised loadSu(n)single‐sided power spectrum of longitudinal wind speed fluctuations, u, at a fixed point
single‐sided power spectrum of longitudinal wind speed fluctuations, u, as seen by a point on a rotating blade (also known as rotationally sampled spectrum)
cross‐spectrum of longitudinal wind speed fluctuations, u, as seen by points at radii r1 and r2 on a rotating blade or rotor (single‐sided)Sv(n)single‐sided power spectrum of lateral wind speed fluctuations, v, at a fixed pointSw(n)single‐sided power spectrum of vertical wind speed fluctuations, w, at a fixed pointSηη (n)single‐sided power spectrum of sea surface elevationttime; gear tooth thickness at critical root section; tower wall thickness; monopole wall thickness; thickness of aerofoil section (maximum)Trotor thrust; duration of discrete gust; wind speed averaging period; wave period for regular waves; time stepTcmean period between wave crestsTppeak wave period, 1/fpTzmean zero crossing wave periodufluctuating component of wind speed in the x direction; induced velocity in upstream direction (as in Figure 4.5); perturbation velocity in x direction (downstream, as in Figure 4.11); in‐plane plate deflection in x direction; gear ratio; water particle velocity in x directionu*friction velocity in boundary layerU∞free‐stream velocityUfree‐stream velocityU, U(t)instantaneous wind speed in the along‐wind direction
mean component of wind speed in the along‐wind direction – typically taken over a period of 10 min or 1 hUaveannual average wind speed at hub heightUDstreamwise velocity at the rotor discUiturbine lower cut‐in wind speedUWstreamwise velocity in the far wakeUe1extreme 3 s gust wind speed with 1 year return periodUe50extreme 3 s gust wind speed with 50 year return periodUturbine upper cut‐out wind speedUrturbine rated wind speed, defined as the wind speed at which the turbine's rated power is reachedUrefreference wind speed defined as 10 min mean wind speed at hub height with 50 year return periodU1strain energy of plate flexureU2in‐plane strain energyvfluctuating component of wind speed in the y direction; induced velocity in y direction; in‐plane plate deflection in y directionVairspeed of an autogyro; streamwise velocity at rotor disc, U∞(l – a) (Section 7.1.15); voltage (shown in bold when complex)VArreactive power volt‐amperes‐reactiveV(t)instantaneous lateral wind speedVAapparent power electrical volt‐amperesVffibre volume fraction in composite materialwfluctuating component of wind speed in the z direction; induced velocity in z direction; out‐of‐plane plate deflection; weighting factor; water particle velocity in z directionw(r)blade shell skin thickness (Section 6.4.2)Wwind velocity relative to a point on rotating blade; electrical power lossxdownwind coordinate – fixed and rotating axis systems; horizontal co‐ordinate in the direction of wave propagation; downwind displacementx(t)stochastic component of a variablexnlength of near wake regionxmode of distribution
1first mode component of steady tip displacementXelectrical inductive reactanceXncoefficient of nth term in Dean's stream functionylateral coordinate with respect to vertical axis (starboard positive) – fixed axis systemylateral coordinate with respect to blade axis – rotating axis systemylateral displacement; reduced variate of distribution; height above seabedzvertical coordinate (upwards positive) – fixed axis system; height above ground datum; height above water level; delay operatorzradial coordinate along blade axis – rotating axis systemzground roughness lengthz1number of teeth on pinion gearz(t)periodic component of a variableZsection modulus; externally applied load on flanged
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