Research Papers

Energy Dissipation in Dynamical Systems Through Sequential Application and Removal of Constraints

[+] Author and Article Information
Jimmy Issa, Alejandro R. Diaz

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226

Ranjan Mukherjee1

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226mukherji@egr.msu.edu

An example of a special situation is where the system of masses move in a manner that maintains x2(t)0; this will occur if one of the modes have a zero displacement for mass m2 and the system vibrates in that mode.

The constrained system can also be described by differential algebraic equations comprised of the original ordinary differential equations in Eq. 4 and the algebraic constraint equation—see Sec. 1.3.4 of Ref. 11, for example.

Alternatively, Eq. 20 can be viewed as a complementarity between the velocity after impact and the impulse.

Such impulsive moments can be generated in experiments by an electromagnetic brake, as in Ref. 10.


Corresponding author.

J. Dyn. Sys., Meas., Control 131(2), 021011 (Feb 09, 2009) (9 pages) doi:10.1115/1.3023126 History: Received December 18, 2007; Revised June 19, 2008; Published February 09, 2009

A strategy to remove energy from finite-dimensional elastic systems is presented. The strategy is based on the cyclic application and removal of constraints that effectively remove and restore degrees of freedom of the system. In general, application of a constraint removes kinetic energy from the system, while removal of the constraint resets the system for a new cycle of constraint application. Conditions that lead to a net loss in kinetic energy per cycle and bounds on the amount of energy removed are presented. In linear systems, these bounds are related to the modes of the system in its two states, namely, with and without constraints. It is shown that energy removal is always possible, even using a random switching schedule, except in one scenario, when energy is trapped in modes that span an invariant subspace with special orthogonality properties. Applications to nonlinear systems are discussed. Examples illustrate the process of energy removal in both linear and nonlinear systems.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

A three degree-of-freedom mass-spring system

Grahic Jump Location
Figure 2

Scenario depicting two masses that stay connected after impact

Grahic Jump Location
Figure 3

A linear system with 3DOF in state α and 2DOF in state β

Grahic Jump Location
Figure 4

Action-reaction pair of impulsive moments

Grahic Jump Location
Figure 5

Plot of displacements of the bars and total energy of the system

Grahic Jump Location
Figure 6

A modified version of the system in Fig. 3 in states α and β

Grahic Jump Location
Figure 7

Plot of modal amplitudes in state α and total energy of the system

Grahic Jump Location
Figure 8

Second mode of vibration of the system in Fig. 6

Grahic Jump Location
Figure 9

An example nonlinear system

Grahic Jump Location
Figure 10

Plot of generalized coordinates and total energy of the nonlinear system



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