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

A correction method for dynamic analysis of linear systems

FAILLA, Giuseppe
2004-01-01

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
Correction method; Particular solution of linear differential equations; Truncated modal analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/5295
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