By Sondipon Adhikari
Since Lord Rayleigh brought the assumption of viscous damping in his vintage paintings "The concept of Sound" in 1877, it has develop into commonplace perform to take advantage of this technique in dynamics, overlaying a variety of functions from aerospace to civil engineering. notwithstanding, within the majority of functional instances this procedure is followed extra for mathematical comfort than for modeling the physics of vibration damping.Over the previous decade, huge learn has been undertaken on extra basic "non-viscous" damping versions and vibration of non-viscously damped platforms. This ebook, besides a comparable e-book Structural Dynamic research with Generalized Damping versions: research, is the 1st entire research to hide vibration issues of common non-viscous damping. the writer attracts on his significant learn event to supply a textual content protecting: parametric senistivity of damped platforms; id of viscous damping; identity of non-viscous damping; and a few instruments for the quanitification of damping. The ebook is written from a vibration concept point of view, with a number of labored examples that are proper throughout a variety of mechanical, aerospace and structural engineering applications.Contents1. Parametric Sensitivity of Damped Systems.2. id of Viscous Damping.3. identity of Non-viscous Damping.4. Quantification of Damping.About the AuthorsSondipon Adhikari is Chair Professor of Aerospace Engineering at Swansea collage, Wales. His wide-ranging and multi-disciplinary study pursuits comprise uncertainty quantification in computational mechanics, bio- and nanomechanics, dynamics of advanced platforms, inverse difficulties for linear and nonlinear dynamics, and renewable strength. he's a technical reviewer of ninety seven overseas journals, 18 meetings and thirteen investment bodies.He has written over a hundred and eighty refereed magazine papers, a hundred and twenty refereed convention papers and has authored or co-authored 15 e-book chapters. �Read more...
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Additional resources for Structural dynamic analysis with generalized damping models : identification
Here, the dissipative element connected between the two masses is not a simple viscous dashpot but a non-viscous damper. 129] and G(t) = g(t)ˆI, where ˆI = 1 −1 . 131] where c is a constant, and μ1 and μ2 are known as the relaxation parameters. 131], if the function associated with c was a delta function, c would be the familiar viscous damping constant. 130], we obtain −1 −1 G(s) = cˆI (1 + s/μ1 ) + (1 + s/μ2 ) . 70] shows that the system has six eigenvalues – four of which occur in complex conjugate pairs and correspond to the two elastic modes.
60] Chapter 5 of [ADH 14], lims→sj νr (s) = 0. 81] with respect to p to obtain ∂Zr (s) ∂ϕ (s) ϕr (s) + Zr (s) r = 0. 97] Premultiplying the above equation by ϕTr (s), we obtain ϕTr (s) ∂Zr (s) ∂ϕ (s) ϕr (s) + ϕTr (s)Zr (s) r = 0. 81] and considering the symmetry property of Zr (s), it follows that the second term of the left-hand side of the above equation is zero. 98] reduces to ϕTr (s) ∂Zr (s) ϕr (s) = 0. 96] has a “0 by 0” form. 96], we obtain ajj = − 2 [D(s)] zTj ∂ ∂s ∂p |s=sj zj r (s) 2 ∂ν∂s |s=sj 2 [D(s)] zTj ∂ ∂s ∂p |s=sj zj .
Conditions that G(s) must satisfy in order to produce dissipative motion were given by Golla and Hughes [GOL 85]. 69] where zj ∈ CN is the jth eigenvector. The eigenvalues, sj , are roots of the characteristic equation det s2 M + s G(s) + K = 0. 70] We consider that the order of the characteristic equation is m. Following Chapter 5 of [ADH 14], we may group the eigenvectors as (1) elastic modes (corresponding to N complex conjugate pairs of eigenvalues), and (2) non-viscous modes (corresponding to the “additional” m − 2N eigenvalues).