Application of the Ritz method to the optimization of vibrating structures

J. Gregory McDaniel, Andrew S. Wixom

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This work presents an application of the Ritz Method to the optimization of vibrating structures. The optimization problems considered here involve local design choices made in various regions of the structure in hopes of improving the vibration characteristics of the structure. In order to find the global optimum, one must perform an exhaustive search over all combinations of such choices. Even a modest number of design choices may give rise to a large number of combinations, so that an exhaustive search becomes computationally intensive. In the present work , the Ritz Method is employed to efficiently compute cost functions related to the vibration characteristics of the structure. Since the Ritz Method is based on integral expressions of the potential and kinetic energies of the structure, one may naturally divide these integrals over regions of the structure. In doing so, the concept of substructuring appears naturally in the formulation without explicitly considering boundary conditions between regions. This advantage, combined with the well-known convergence properties of the Ritz Method, provide for a computationally efficient approach for optimization problems. Numerical examples related to the optimization of a vibrating plate illustrate the approach.

Original languageEnglish (US)
Title of host publicationASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012
Pages465-471
Number of pages7
DOIs
StatePublished - Dec 1 2012
EventASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012 - New York City, NY, United States
Duration: Aug 19 2012Aug 22 2012

Publication series

NameAmerican Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCAD

Other

OtherASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012
CountryUnited States
CityNew York City, NY
Period8/19/128/22/12

Fingerprint

optimization
vibration
Potential energy
Kinetic energy
Cost functions
kinetic energy
potential energy
Boundary conditions
boundary conditions
costs
formulations

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Acoustics and Ultrasonics

Cite this

McDaniel, J. G., & Wixom, A. S. (2012). Application of the Ritz method to the optimization of vibrating structures. In ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012 (pp. 465-471). (American Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCAD). https://doi.org/10.1115/NCAD2012-1211
McDaniel, J. Gregory ; Wixom, Andrew S. / Application of the Ritz method to the optimization of vibrating structures. ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. 2012. pp. 465-471 (American Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCAD).
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McDaniel, JG & Wixom, AS 2012, Application of the Ritz method to the optimization of vibrating structures. in ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. American Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCAD, pp. 465-471, ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012, New York City, NY, United States, 8/19/12. https://doi.org/10.1115/NCAD2012-1211

Application of the Ritz method to the optimization of vibrating structures. / McDaniel, J. Gregory; Wixom, Andrew S.

ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. 2012. p. 465-471 (American Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCAD).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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McDaniel JG, Wixom AS. Application of the Ritz method to the optimization of vibrating structures. In ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. 2012. p. 465-471. (American Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCAD). https://doi.org/10.1115/NCAD2012-1211