doc LEReSp
Documentation of the LEReSp function.
helpFun('LEReSp')
Linear Elastic Response Spectra
[PSA,PSV,SD,SV,SA,SIEV]=LERESP(DT,XGTT,T,KSI,DTTOL,...
ALGID,RINF)
Description
The linear elastic response spectra for a given time-history of
constant time step, a given eigenperiod range and a given viscous
damping ratio are computed. These spectra include the spectral
acceleration, spectral velocity, spectral displacement,
pseudoacceleration, pseudovelocity, absolute equivalent input energy
velocity and relative equivalent input energy velocity. This function
is part of the OpenSeismoMatlab software. It can be used as
standalone, however attention is needed for the correctness of the
input arguments, since no checks are performed in this function. See
the example example_LEReSp.m for more details about how this function
can be implemented.
Input parameters
DT [double(1 x 1)] is the time step of the input acceleration time
history XGTT.
XGTT [double(1:numsteps x 1)] is the input acceleration time history.
numsteps is the length of the input acceleration time history.
T [double(1:numSDOFs x 1)] contains the values of eigenperiods for
which the response spectra are requested. numSDOFs is the number
of SDOF oscillators being analysed to produce the spectra.
KSI [double(1 x 1)] is the fraction of critical viscous damping.
DTTOL [double(1 x 1)] is the maximum ratio of the integration time
step to the eigenperiod.
ALGID [char(1 x :inf)] is the algorithm to be used for the time
integration. It can be one of the following strings for superior
optimally designed algorithms:
'generalized a-method': The generalized a-method (Chung &
Hulbert, 1993)
'HHT a-method': The Hilber-Hughes-Taylor method (Hilber,
Hughes & Taylor, 1977)
'WBZ': The Wood–Bossak–Zienkiewicz method (Wood, Bossak &
Zienkiewicz, 1980)
'U0-V0-Opt': Optimal numerical dissipation and dispersion
zero order displacement zero order velocity algorithm
'U0-V0-CA': Continuous acceleration (zero spurious root at
the low frequency limit) zero order displacement zero order
velocity algorithm
'U0-V0-DA': Discontinuous acceleration (zero spurious root at
the high frequency limit) zero order displacement zero order
velocity algorithm
'U0-V1-Opt': Optimal numerical dissipation and dispersion
zero order displacement first order velocity algorithm
'U0-V1-CA': Continuous acceleration (zero spurious root at
the low frequency limit) zero order displacement first order
velocity algorithm
'U0-V1-DA': Discontinuous acceleration (zero spurious root at
the high frequency limit) zero order displacement first order
velocity algorithm
'U1-V0-Opt': Optimal numerical dissipation and dispersion
first order displacement zero order velocity algorithm
'U1-V0-CA': Continuous acceleration (zero spurious root at
the low frequency limit) first order displacement zero order
velocity algorithm
'U1-V0-DA': Discontinuous acceleration (zero spurious root at
the high frequency limit) first order displacement zero order
velocity algorithm
'Newmark ACA': Newmark Average Constant Acceleration method
'Newmark LA': Newmark Linear Acceleration method
'Newmark BA': Newmark Backward Acceleration method
'Fox-Goodwin': Fox-Goodwin formula
RINF [double(1 x 1)] is the minimum absolute value of the eigenvalues
of the amplification matrix. For the amplification matrix see
eq.(61) in Zhou & Tamma (2004).
Output parameters
PSA [double(1:numSDOFs x 1)] is the Pseudo Acceleration Spectrum.
PSV [double(1:numSDOFs x 1)] is the Pseudo Velocity Spectrum.
SD [double(1:numSDOFs x 1)] is the Spectral Displacement.
SV [double(1:numSDOFs x 1)] is the Spectral Velocity.
SA [double(1:numSDOFs x 1)] is the Spectral Acceleration.
SIEV [double(1:numSDOFs x 1)] is the equivalent relative input
energy velocity. See: {Uang, C. M., & Bertero, V. V. (1990).
Evaluation of seismic energy in structures. Earthquake
engineering & structural dynamics, 19(1), 77-90} for more
details.
Example
dt=0.02;
N=10;
a=rand(N,1)-0.5;
b=100*pi*rand(N,1);
c=pi*(rand(N,1)-0.5);
t=(0:dt:(100*dt))';
xgtt=zeros(size(t));
for i=1:N
xgtt=xgtt+a(i)*sin(b(i)*t+c(i));
end
T=logspace(log10(0.02),log10(50),1000)';
ksi=0.05;
dtTol=0.02;
AlgID='U0-V0-Opt';
rinf=1;
[PSa,PSv,Sd,Sv,Sa,Siev]=LEReSp(dt,xgtt,T,ksi,dtTol,...
AlgID,rinf);
__________________________________________________________________________
Copyright (c) 2018-2023
George Papazafeiropoulos
Major, Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D.
Email: gpapazafeiropoulos@yahoo.gr
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