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A modified modal analysis method for damped multi‐degree‐of‐freedom‐systems in structural mechanics
Author(s) -
Stanoev Evgueni
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300061
Subject(s) - eigenvalues and eigenvectors , modal , modal analysis using fem , equations of motion , modal matrix , modal testing , matrix (chemical analysis) , modal analysis , mathematics , damping matrix , transformation (genetics) , degrees of freedom (physics and chemistry) , mathematical analysis , transformation matrix , computer science , classical mechanics , vibration , symmetric matrix , physics , finite element method , stiffness matrix , structural engineering , kinematics , diagonalizable matrix , acoustics , engineering , materials science , chemistry , composite material , biochemistry , polymer chemistry , gene , quantum mechanics
A general method for the modal decomposition of the equations of motion of damped multi‐degree‐of‐freedom‐systems is presented. The first variant of the presented method in earlier publications of the author, including the complex right eigenvectors, is briefly reviewed first. The second presented variant is also based on the corresponding eigenvalue problem of the damped structure including the complex left and right eigenvectors. After initial partitioning of the equations of motion a real modal transformation matrix is built by a combination of two complex transformations. For the general case of damped structures with non‐modal symmetric damping matrix a modal analysis can be performed in real arithmetic. Two numerical examples with 3 and 10 DOF's demonstrate the accuracy and the advantages of the presented modal solution method.