Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Energy equipartition and fluctuation-dissipation theorems for damped flexible structures

Authors: Ronald K. Pearson and Timothy L. Johnson
Journal: Quart. Appl. Math. 45 (1987), 223-238
MSC: Primary 73K35; Secondary 34F05
DOI: https://doi.org/10.1090/qam/895095
MathSciNet review: 895095
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Dynamics and control of flexible mechanical structures has been the topic of much recent research. Here, we examine the energy distribution in finite-dimensional flexible structure models of the type obtained through finite element analysis. Modeling external disturbance forces as zero-mean white noise, we establish that symmetry of the damping matrix is a sufficient condition for the equipartition of potential and kinetic energy in the structure. In addition, we develop upper and lower bounds on the total energy stored in symmetrically damped structures in terms of the strength of the stochastic driving term and the Euclidean norms of the damping matrix and its inverse. In two special cases, explicit solutions for the total energy are obtained and may be viewed as fluctuation-dissipation theorems for the structure models. Convergence conditions for modal expansions of distributed parameter flexible structure models are then developed from these finite-dimensional results. These conditions are interpreted physically as interrelations between assumed damping mechanisms and disturbance force actuator models that must exist in formulating well-posed stochastic distributed-parameter flexible structure models.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73K35, 34F05

Retrieve articles in all journals with MSC: 73K35, 34F05

Additional Information

DOI: https://doi.org/10.1090/qam/895095
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society