0
Research Papers

The Method of Receptances for Continuous Rods

[+] Author and Article Information
Amit Maha

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: amaha@tigers.lsu.edu

Y. M. Ram

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: ram@me.lsu.edu

We used the first three numbers generated by MATLAB pseudo random number generator after invoking the software.

Manuscript received January 7, 2014; final manuscript received April 3, 2014; accepted manuscript posted April 9, 2014; published online April 21, 2014. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(7), 071009 (Apr 21, 2014) (7 pages) Paper No: JAM-14-1020; doi: 10.1115/1.4027370 History: Received January 07, 2014; Revised April 03, 2014; Accepted April 09, 2014

It is shown that it is possible in general to assign 2n poles of an axially vibrating nonuniform rod by sensing the state at n points along the rod and by using an actuator which applies the control force. Moreover, the assignment of poles may be done without continuous or discrete analytical modeling. In particular, the rigidity, the density, and the variable cross-sectional area of the rod may be considered unknown. The control gains are determined by the receptances between the point of actuation and the points of sensing, which may be measured experimentally. In the analytical arena, where the receptances are exact, the assignment of the desired poles is also exact and suffers from no discretization or model reduction errors. However, the control force affects in general the distribution of the poles which are not intended to be desirably placed or to remain unchanged. Although the analysis is carried out for simplicity on an axially vibrating rod, the above mentioned results are generally applicable to other linear elastic structures of higher dimensions.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Closed loop system

Grahic Jump Location
Fig. 2

Exponential excitation

Grahic Jump Location
Fig. 4

Frequency function of the closed loop uniform rod

Grahic Jump Location
Fig. 5

Frequency function of the closed loop exponential rod

Grahic Jump Location
Fig. 6

Frequency functions of the open and closed loops exponential rod

Grahic Jump Location
Fig. 7

Rod with multiple actuators

Grahic Jump Location
Fig. 8

(a) Transversely vibrating beam and (b) vibrating plate

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In