ModalAnalysis

Purpose

determines modal response history for given transient loading

Synopsis

[omega,Ueig,Y_t,Ydot_t,Yddot_t] = ModalAnalysis (option,Kf,M,Loading,Deltat,zeta,nmod)

Description

MODALANALYSIS determines modal response history for given transient loading
  [OMEGA,UEIG,Y_T,YDOT_T,YDDOT_T] = MODALANALYSIS (OPTION,KF,M,LOADING,DELTAT,ZETA,NMOD)
  the function determines the response history of a multi-dof structural model
  with stiffness matrix at free dofs KF and consistent mass matrix or lumped mass vector M
  under given transient loading in data structure LOADING
  for the lowest NMOD (default=all) eigenmodes or NMOD Ritz vectors
  with damping ratios in row vector ZETA (default=0);
  the time step of integration is DELTAT;
        OPTION = 'eig'  uses nmod eigenvectors,
  while OPTION = 'Ritz' uses nmod Ritz vectors in the modal analysis; 
  the function returns NMOD eigenfrequencies of the structural model in row vector OMEGA,
  the eigenmode or Ritz vector shapes in array UEIG arranged columnwise (column no=mode no),
  and the response history of each eigenmode or Ritz vector
  in array Y_T arranged columnwise (column no=mode no),
  the velocity history of each eigenmode or Ritz vector in array YDOT_t, and
  the acceleration history of each eigenmode or Ritz vector in array YDDOT_t
  the data structure LOADING has the following fields
  LOADING.Uddref = vector of reference acceleration values at model dofs
          Pref   = vector of reference load         values at model dofs
          U0     = vector of initial displacement   values at model dofs
          Udot0  = vector of initial velocity       values at model dofs
          FrcHst = force time history in field Value
          AccHst = acceleration time history in field Value

Cross-Reference Information

This function calls:

• EigenMode determines eigenfrequencies and eigenmodes of structural model
• LDRitzVectors generation of mass and stiffness orthogonal Load Dependent Ritz vectors
• LSDOF_LinearWilson transient response of linear SDOF system by exact integration of piecewise linear excitation
• ModeDecomposition determines eigenmode participation factors of given vector V