doc DRHA

Documentation of the DRHA function.

helpFun('DRHA')

 Dynamic Response History Analysis

 [U,V,A,F,ES,ED] = DRHA(K,M,DT,XGTT,KSI,U0,UT0,ALGID,RINF)

 Description
     Calculate the dynamic response of a linear MDOF system using modal
     analysis. 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_DRHA.m for more details about
     how this function can be implemented.

 Input parameters
     K [double(:inf x 1)] is the stiffness of the system.
     M [double(:inf x 1)] is the lumped masses of the structure.
     DT [double(1 x 1)] is the time step of the dynamic response history
         analysis
     XGTT [double(1:nstep x 1)]: column vector of the acceleration history
         of the excitation imposed at the base. nstep is the number of
         time steps of the dynamic response.
     KSI [double(1 x 1)] is the ratio of critical damping of the SDOF
         system.
     U0 [double(:inf x 1)] is the initial displacement of the SDOF system.
     UT0 [double(:inf x 1)] is the initial velocity of the SDOF system.
     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
     U [double(1 x 1:nstep)]: displacement time history.
     V [double(1 x 1:nstep)]: velocity time history.
     A [double(1 x 1:nstep)]: acceleration time history.
     F [double(1 x 1:nstep)]: equivalent static force time history.
     ES [double(1 x 1:nstep)]: time-history of the recoverable
         strain energy of the system (total and not incremental).
     ED [double(1 x 1:nstep)]: time-history of the energy
         dissipated by viscoelastic damping during each time step
         (incremental). cumsum(Ed) gives the time history of the total
         energy dissipated at dof i from the start of the dynamic
         analysis.

__________________________________________________________________________
 Copyright (c) 2018-2023
     George Papazafeiropoulos
     Major, Infrastructure Engineer, Hellenic Air Force
     Civil Engineer, M.Sc., Ph.D.
     Email: gpapazafeiropoulos@yahoo.gr
 _________________________________________________________________________

Published with MATLAB® R2022b