Euler-Maclaurin Closed Form Finite State Space Model for a String Applied to Broadband Plate Vibrations
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-05-05
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
The Euler-Maclaurin sun formula is applied to the infinite series Green's function solution in the space-time Laplace transform domain for the one dimensional wave equation for a string fixed at each end.
The resulting approximate closed form solution is used to derive a single third order input-output ordinary differential equation to model the string dynamics.
The average modal density of a plate is shown to be comparable to a string.
A finite three state-space model is developed for the string and applied to the vibrations of a plate subjected to broadband random and impulse inputs.
The applications include the direct problem of determining the response to a disturbance input and the inverse problem of identifying the disturbance input with a finite state observer based on the finite string model.
Numerical simulations using many plate modes are obtained in the time and frequency domains and are used to compare the multimodal plate model to the finite string based model and to demonstrate how the finite string based model can be used to represent the multimodal vibrations of the plate.
American Psychological Association (APA)
Panza, Michael J.. 2010. Euler-Maclaurin Closed Form Finite State Space Model for a String Applied to Broadband Plate Vibrations. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-500478
Modern Language Association (MLA)
Panza, Michael J.. Euler-Maclaurin Closed Form Finite State Space Model for a String Applied to Broadband Plate Vibrations. Mathematical Problems in Engineering No. 2010 (2010), pp.1-14.
https://search.emarefa.net/detail/BIM-500478
American Medical Association (AMA)
Panza, Michael J.. Euler-Maclaurin Closed Form Finite State Space Model for a String Applied to Broadband Plate Vibrations. Mathematical Problems in Engineering. 2010. Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-500478
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-500478