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Response of non‐classically damped structures in the modal subspace
Author(s) -
D'Aveni Antonino,
Muscolino Giuseppe
Publication year - 1995
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290240907
Subject(s) - eigenvalues and eigenvectors , modal , subspace topology , damping matrix , superposition principle , modal analysis using fem , mathematics , modal analysis , operator (biology) , matrix (chemical analysis) , modal matrix , modal testing , mathematical analysis , algorithm , stiffness matrix , finite element method , structural engineering , physics , symmetric matrix , engineering , diagonalizable matrix , materials science , repressor , chemistry , composite material , biochemistry , quantum mechanics , transcription factor , polymer chemistry , gene
The evaluation of the dynamic response of non‐classically damped linear structures requires the solution of an eigenproblem with complex eigenvalues and modal shapes. Since in practice only a small number of complex modes are needed, the complex eigenvalue problem is solved in the modal subspace in which the generalized damping matrix is not uncoupled by classical real modes. It follows that the evaluation of the structural response requires in both cases the determination of complex modes by numerical techniques, which are not as robust as techniques currently used for the solution of the real eigenvalue problem, and the use of complex algebra. In the present paper an unconditionally stable step‐by‐step procedure is presented for the response of non‐classically damped structures in the modal subspace without using complex quantities. The method is based on the evaluation of the fundamental operator in approximated form of the numerical procedure. In addition, the method can be easily modified to incorporate the modal superposition pseudo‐static correction terms.