A correction method for dynamic analysis of linear systems

Risultato della ricerca: Article

17 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)1217-1226
Numero di pagine10
RivistaCOMPUTERS & STRUCTURES
Volume82
Stato di pubblicazionePublished - 2004

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Modal analysis
Dynamic Analysis
Dynamic analysis
Dynamic response
Linear systems
Linear Systems
Derivatives
Convergence Condition
Modal Analysis
Computing
Particular Solution
Series Expansion
Dynamic Response
Analytical Methods
Damped
Degree of freedom
First-order
Derivative
Unknown
Series

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Modelling and Simulation
  • Materials Science(all)
  • Mechanical Engineering
  • Computer Science Applications

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A correction method for dynamic analysis of linear systems. / Di Paola, Mario.

In: COMPUTERS & STRUCTURES, Vol. 82, 2004, pag. 1217-1226.

Risultato della ricerca: Article

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AB - 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.

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