Hamilton, Ritz, and ElastodynamicsSource: Journal of Applied Mechanics:;1976:;volume( 043 ):;issue: 004::page 684Author:C. D. Bailey
DOI: 10.1115/1.3423956Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The theory of Ritz is applied to the equation that Hamilton called the “Law of Varying Action.” Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin’s principles for linear elastodynamics. A brief discussion of Hamilton’s law and Hamilton’s principle is followed by examples of results for both free-free and cantilever beams with various loadings.
keyword(s): Elastodynamics , Equations , Free vibrations , Cantilever beams , Motion , Hamilton's principle AND Differential equations ,
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| contributor author | C. D. Bailey | |
| date accessioned | 2017-05-08T22:59:59Z | |
| date available | 2017-05-08T22:59:59Z | |
| date copyright | December, 1976 | |
| date issued | 1976 | |
| identifier issn | 0021-8936 | |
| identifier other | JAMCAV-26065#684_1.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/88244 | |
| description abstract | The theory of Ritz is applied to the equation that Hamilton called the “Law of Varying Action.” Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin’s principles for linear elastodynamics. A brief discussion of Hamilton’s law and Hamilton’s principle is followed by examples of results for both free-free and cantilever beams with various loadings. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | Hamilton, Ritz, and Elastodynamics | |
| type | Journal Paper | |
| journal volume | 43 | |
| journal issue | 4 | |
| journal title | Journal of Applied Mechanics | |
| identifier doi | 10.1115/1.3423956 | |
| journal fristpage | 684 | |
| journal lastpage | 688 | |
| identifier eissn | 1528-9036 | |
| keywords | Elastodynamics | |
| keywords | Equations | |
| keywords | Free vibrations | |
| keywords | Cantilever beams | |
| keywords | Motion | |
| keywords | Hamilton's principle AND Differential equations | |
| tree | Journal of Applied Mechanics:;1976:;volume( 043 ):;issue: 004 | |
| contenttype | Fulltext |