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Response of linear slowly varying systems under external excitations

Authors
Journal
Journal of Sound and Vibration
0022-460X
Publisher
Elsevier
Publication Date
Volume
131
Issue
2
Identifiers
DOI: 10.1016/0022-460x(89)90489-6

Abstract

Abstract An approximate closed-form solution for a linear slowly varying system under external excitation is derived. The derivation of the solution is based on the technique of freezing slowly varying parameters, a technique used in establishing the stability of slowly varying homogeneous systems. The error between the approximate and exact solutions is given, and an upper bound on the norm of the error in terms of a measure of the rate of change of the system matrix and the norm of the exact solution of the system is derived. Approximate responses of two particular linear slowly varying systems under external excitation are obtained by the proposed technique; good agreement between the approximate and numerically obtained solutions is observed.

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