- #1
Ronankeating
- 63
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hi all,
Having those input in hand, mass ([M]) n*n matrix , stiffness ([K]) n*n matrices and having obtained the eigen-values, eigenvectors for the higher-frequencies with subspace or simlutaneous iteration respectively, eigen-values ([[itex]\Phi[/itex]]) as m*m diagonal matrix, and m*m eigen-vectors as ([Ω]).
To summarize the inputs:
n = the total DoFs in system
m = number of interested modes (m<n)
M = Mass matrix (n*n)
K = Stiffness matrix (n*n)
[itex]\Phi[/itex]=eigen value matrix (m*m diagonal)
Ω=eigen-vectors (m*m)
How am I supposed to find the that m number of modes are enough for modal analysis for the given case?
Generally in books suggest that, modal particiaption factors are (MPF) = R*[itex]\Phi[/itex]nT / ( [itex]\Phi[/itex]nT*M*[itex]\Phi[/itex]n ) where R is the time independent spatial loading type of external loads( p(t) = R*f (t) ).
But we are interested with eigen-solution of the problem, so there is no any external loading and reasonably there is no R spatial vector. So what actually is book referring with that p(t) = R*f (t) description ?
Regards,
Having those input in hand, mass ([M]) n*n matrix , stiffness ([K]) n*n matrices and having obtained the eigen-values, eigenvectors for the higher-frequencies with subspace or simlutaneous iteration respectively, eigen-values ([[itex]\Phi[/itex]]) as m*m diagonal matrix, and m*m eigen-vectors as ([Ω]).
To summarize the inputs:
n = the total DoFs in system
m = number of interested modes (m<n)
M = Mass matrix (n*n)
K = Stiffness matrix (n*n)
[itex]\Phi[/itex]=eigen value matrix (m*m diagonal)
Ω=eigen-vectors (m*m)
How am I supposed to find the that m number of modes are enough for modal analysis for the given case?
Generally in books suggest that, modal particiaption factors are (MPF) = R*[itex]\Phi[/itex]nT / ( [itex]\Phi[/itex]nT*M*[itex]\Phi[/itex]n ) where R is the time independent spatial loading type of external loads( p(t) = R*f (t) ).
But we are interested with eigen-solution of the problem, so there is no any external loading and reasonably there is no R spatial vector. So what actually is book referring with that p(t) = R*f (t) description ?
Regards,
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