1981
DOI: 10.1002/eqe.4290090205
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Modal methods in the dynamics of systems with non‐classical damping

Abstract: When damping in a system is both significantly high and its distribution is non-classical the solution of dynamical problems by conventional modal analysis is complicated by the presence of coupling between the normal co-ordinates. Further, the convergence of a solution may be erratic with successive modal additions, leading to the need to include a larger number ofmodes than would otherwise be expected. Jn this paper methods of modal analysis in structural dynamics are discussed and their derivations briefly … Show more

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Cited by 52 publications
(8 citation statements)
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“…In this section we study the relationships between the approximations proposed in the previous section when damping is classical, that is when is diagonal in equation (10).…”
Section: Classical Damping and Its Effectsmentioning
confidence: 98%
“…In this section we study the relationships between the approximations proposed in the previous section when damping is classical, that is when is diagonal in equation (10).…”
Section: Classical Damping and Its Effectsmentioning
confidence: 98%
“…In this section both the integral and incremental solution procedures are described for the evaluation of the response of equation (6).…”
Section: Modal Analysismentioning
confidence: 99%
“…where y (t) is the particular solution of equation (6) and y,(t) is a corrective displacement representing the effect otthe initial condition, given as I being the vector of constants depending on initial conditions at time t = to and E (t) a matrix representing the homogeneous solution' of equation (6). The kth and (k + 1)th columns of E(t) are given as l o Y , W = E(t)l (10) where +k and X k are the real and imaginary parts of the kth eigenvector of the matrix D, respectively, and in which Bk and Y k are the real and imaginary parts of the kth eigenvalue associated with the kth eigenvector, respectively.…”
Section: Integral Solutionmentioning
confidence: 99%
“…In case of coupled analysis, the combined eigenproperties of the primary-secondary (P-S) system are determined by considering the two sub-systems as a single dynamic unit and then modal analysis is carried out for getting various responses (see e.g. References [1][2][3][4][5][6]). Since the masses and sti nesses of a secondary system are usually very small compared to those of a primary system, there may be ill-conditioning of matrices in these methods.…”
Section: Introductionmentioning
confidence: 99%