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Higher order eigensensitivities‐based numerical method for the harmonic analysis of viscoelastically damped structures
Author(s) -
MartinezAgirre M.,
Elejabarrieta M. J.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3222
Subject(s) - eigenvalues and eigenvectors , harmonic , superposition principle , computation , damping matrix , modal analysis , fundamental frequency , cantilever , numerical analysis , mathematics , mathematical analysis , damping ratio , frequency response , control theory (sociology) , vibration , finite element method , physics , computer science , algorithm , structural engineering , engineering , acoustics , stiffness matrix , electrical engineering , quantum mechanics , control (management) , artificial intelligence
This paper presents an efficient numerical method for the harmonic analysis of viscoelastically damped structural systems characterized by a frequency‐dependent structural damping matrix, making use of the complex mode superposition method. Departing from the undamped eigensolution, the proposed numerical method updates the complex and frequency‐dependent eigenpair avoiding the solution of a complex eigenproblem for each computational frequency. The complex eigenvalues and eigenvectors are updated within the desired tolerance by an adaptive step‐size control scheme using the first‐ and higher order eigenderivatives. The influence on the computation time of the considered number of eigenderivatives and the tolerance is discussed, and the efficiency of the proposed numerical method for the harmonic analysis of viscoelastically damped large‐ordered structural systems is proved. Finally, a practical application is presented where the harmonic response of a constrained layer damping cantilever beam subjected to a base motion is analyzed. The complex and frequency‐dependent eigenvalues and eigenvectors are computed, the modal contributions to the total response are determined, and the total response is approximated by the complex mode superposition method. Finally, the approximated response is validated with the exact one computed by the direct frequency method and with that experimentally measured. Copyright © 2011 John Wiley & Sons, Ltd.