Application of Ultraspherical Polynomials to Nonlinear Forced OscillationsSource: Journal of Applied Mechanics:;1967:;volume( 034 ):;issue: 001::page 223Author:Y. King Liu
DOI: 10.1115/1.3607636Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Approximate solutions to the conservative free-oscillation problem were obtained recently [1–4] through the use of ultraspherical polynomials. The present paper extends the technique to forced oscillations governed by ẍ + g(ẋ) + f(x) = F0 sin pt + F1 Very accurate results are obtained either by setting the ultraspherical polynomial index λ = 0 or, better yet, by restricting the choice of λ such that the solution to the forced problem is a perturbation from the nonlinear free oscillation solution. Examples are given.
keyword(s): Oscillations AND Polynomials ,
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| contributor author | Y. King Liu | |
| date accessioned | 2017-05-08T23:51:47Z | |
| date available | 2017-05-08T23:51:47Z | |
| date copyright | March, 1967 | |
| date issued | 1967 | |
| identifier issn | 0021-8936 | |
| identifier other | JAMCAV-25844#223_1.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/117756 | |
| description abstract | Approximate solutions to the conservative free-oscillation problem were obtained recently [1–4] through the use of ultraspherical polynomials. The present paper extends the technique to forced oscillations governed by ẍ + g(ẋ) + f(x) = F0 sin pt + F1 Very accurate results are obtained either by setting the ultraspherical polynomial index λ = 0 or, better yet, by restricting the choice of λ such that the solution to the forced problem is a perturbation from the nonlinear free oscillation solution. Examples are given. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | Application of Ultraspherical Polynomials to Nonlinear Forced Oscillations | |
| type | Journal Paper | |
| journal volume | 34 | |
| journal issue | 1 | |
| journal title | Journal of Applied Mechanics | |
| identifier doi | 10.1115/1.3607636 | |
| journal fristpage | 223 | |
| journal lastpage | 226 | |
| identifier eissn | 1528-9036 | |
| keywords | Oscillations AND Polynomials | |
| tree | Journal of Applied Mechanics:;1967:;volume( 034 ):;issue: 001 | |
| contenttype | Fulltext |