sensitivity of eigenvalues to nonsymmetrical, dissipative control matrices
Clicks: 172
ID: 148550
1993
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This
article has not been analysed, so there is no overall score —
reader engagement is measured and shown alongside.
Reader Engagement
Star Article
30.0
/100
172 views
62 readers
AI Quality Assessment
Not analyzed
Readership in this journal
StarRanked #87 of 275 articles by views in Nano letters
Most read
Least read
Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 275 in total.
Mint this article as an NFT
Not yet mintedCreate a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.
5
SUSD
one-off · no wallet required
Abstract
Dissipation of energy in vibrating structures can be accomplished with a combination of passive damping and active, constant gain, closed loop control forces. The matrix equations are Mz¨+Cz˙+Kz=−Gz˙. With conventional viscous damping, the damping force is proportional to relative velocity, with Fi=Ciiz˙i−Cijz˙j, where Cii=Cij but the subscripts show the position of the number in the C matrix. For a dashpot connected directly to ground, Fi=Ciiz˙i. Thus there is a definite pattern to the positions of numbers in the ith and jth rows of the C matrix, that is, a positive number on the diagonal is paired with an equal negative number, or zero, off the diagonal. With the control matrix G, it is here assumed that the positioning of individual controllers and sensors is flexible, with Fi=Ciiz˙i or Fi=Cijz˙j, the latter meaning that the control force at i is proportional to the velocity sensed at j. Thus the problem addressed herein is how the individual elements in the G matrix affect the modal eigenvalues. Two methods are discussed for finding the sensitivities, the classical method based on the products of eigenvectors and a new method, derived during the present study, involving the derivatives of the invariants in the similarity transformation. Examples are presented for the sensitivities of the complex eigenvalues of the form λr=−ζrwr+iwDr to individual elements in the G matrix, to combinations of elements, and to a combination of passive damping and active control. Systems with two, three, and eight degrees of freedom are investigated.
| Reference Key |
neubert1993shocksensitivity
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | ;Vernon H. Neubert |
| Journal | Nano letters |
| Year | 1993 |
| DOI |
10.3233/SAV-1993-1206
|
| URL | |
| Keywords |
Citations
No citations found. To add a citation, contact the admin at info@scimatic.org
Comments
No comments yet. Be the first to comment on this article.