Mathematica solution of Rayleigh equation in non-linear vibration.
Saved in:
| Title: | Mathematica solution of Rayleigh equation in non-linear vibration. |
|---|---|
| Authors: | Mikhailov, M. D.1 mikhailov@lttc.coppe.ufrj.br |
| Source: | Communications in Numerical Methods in Engineering. May2003, Vol. 19 Issue 5, p401-406. 6p. 1 Chart, 4 Graphs. |
| Subjects: | Wolfram language (Computer program language), Rayleigh number, Vibration measurements, Vibrational spectra, Differential equations |
| Abstract: | The stable periodic motion, described by Rayleigh differential equation, is solved by using the Mathematica software system. We define rules computing the periods T, the magnitude A, the displacement u(t), and the velocity v(t) for prescribed perturbation parameter ℇ and circular frequency ω. These rules have been explored to find the period T, the magnitude A, and the reducing factor of the circular frequency α=2π/T with 10 correct digits after decimal point for ω equal to 1 and the values of ℇ in the range from 0.1 to 100. The displacement and the velocity are plotted for ℇ equal to 0.1, 1, 10, and 100. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] |
| Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 13508694 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Mathematica solution of Rayleigh equation in non-linear vibration. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mikhailov%2C+M%2E+D%2E%22">Mikhailov, M. D.</searchLink><relatesTo>1</relatesTo><i> mikhailov@lttc.coppe.ufrj.br</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Communications+in+Numerical+Methods+in+Engineering%22">Communications in Numerical Methods in Engineering</searchLink>. May2003, Vol. 19 Issue 5, p401-406. 6p. 1 Chart, 4 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Wolfram+language+%28Computer+program+language%29%22">Wolfram language (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Rayleigh+number%22">Rayleigh number</searchLink><br /><searchLink fieldCode="DE" term="%22Vibration+measurements%22">Vibration measurements</searchLink><br /><searchLink fieldCode="DE" term="%22Vibrational+spectra%22">Vibrational spectra</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The stable periodic motion, described by Rayleigh differential equation, is solved by using the Mathematica software system. We define rules computing the periods T, the magnitude A, the displacement u(t), and the velocity v(t) for prescribed perturbation parameter ℇ and circular frequency ω. These rules have been explored to find the period T, the magnitude A, and the reducing factor of the circular frequency α=2π/T with 10 correct digits after decimal point for ω equal to 1 and the values of ℇ in the range from 0.1 to 100. The displacement and the velocity are plotted for ℇ equal to 0.1, 1, 10, and 100. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=13508694 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/cnm.599 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 6 StartPage: 401 Subjects: – SubjectFull: Wolfram language (Computer program language) Type: general – SubjectFull: Rayleigh number Type: general – SubjectFull: Vibration measurements Type: general – SubjectFull: Vibrational spectra Type: general – SubjectFull: Differential equations Type: general Titles: – TitleFull: Mathematica solution of Rayleigh equation in non-linear vibration. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mikhailov, M. D. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2003 Type: published Y: 2003 Identifiers: – Type: issn-print Value: 10698299 Numbering: – Type: volume Value: 19 – Type: issue Value: 5 Titles: – TitleFull: Communications in Numerical Methods in Engineering Type: main |
| ResultId | 1 |
