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Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis (Paperback)
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Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis (Paperback)
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A method of dynamic substructuring is presented which utilizes a
set of static Ritz vectors as a replacement for normal eigenvectors
in component mode synthesis. This set of Ritz vectors is generated
in a recurrence relationship, proposed by Wilson, which has the
form of a block-Krylov subspace. The initial seed to the recurrence
algorithm is based upon the boundary flexibility vectors of the
component. Improvements have been made in the formulation of the
initial seed to the Krylov sequence, through the use of
block-filtering. A method to shift the Krylov sequence to create
Ritz vectors that will represent the dynamic behavior of the
component at target frequencies, the target frequency being
determined by the applied forcing functions, has been developed. A
method to terminate the Krylov sequence has also been developed.
Various orthonormalization schemes have been developed and
evaluated, including the Cholesky/QR method. Several auxiliary
theorems and proofs which illustrate issues in component mode
synthesis and loss of orthogonality in the Krylov sequence have
also been presented. The resulting methodology is applicable to
both fixed and free- interface boundary components, and results in
a general component model appropriate for any type of dynamic
analysis. The accuracy is found to be comparable to that of
component synthesis based upon normal modes, using fewer
generalized coordinates. In addition, the block-Krylov recurrence
algorithm is a series of static solutions and so requires
significantly less computation than solving the normal eigenspace
problem. The requirement for less vectors to form the component,
coupled with the lower computational expense of calculating these
Ritz vectors, combine to create a method more efficient than
traditional component mode synthesis.
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