6533b837fe1ef96bd12a335c
RESEARCH PRODUCT
A correction method for dynamic analysis of linear systems
Giuseppe FaillaMario Di Paolasubject
Basis (linear algebra)Series (mathematics)Particular solution of linear differential equationMechanical EngineeringModal analysis using FEMModal analysisLinear systemCorrection methodComputer Science ApplicationsMethod of undetermined coefficientsControl theoryModeling and SimulationConvergence (routing)Applied mathematicsGeneral Materials ScienceSeries expansionCivil and Structural EngineeringMathematicsTruncated modal analysisdescription
Abstract This paper proposes an analytical method to improve the accuracy of the dynamic response of classically damped linear systems, as given by a standard truncated modal analysis. Upon computing the first m undamped modes of a n-degree-of-freedom system, two sets of equations in the Rn nodal space are built, which are uncoupled and govern the contribution to the response of the m computed modes and the remaining (n−m) unknown modes, respectively. The first set is solved in the Rm modal space by using the m available modes; the second set is solved in a reduced R(n−m) nodal space, without computing additional modes. Specifically, it is shown that the particular solution of the second set of equations may be obtained by a series expansion involving repetitive time derivatives of the first-order static solution. The convergence conditions of such a series are discussed and proved on a rigorous basis. Numerical applications are also presented to demonstrate the effectiveness of the proposed method.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-06-01 |