The Normal Modes of Nonlinear n-Degree-of-Freedom SystemsSource: Journal of Applied Mechanics:;1962:;volume( 029 ):;issue: 001::page 7Author:R. M. Rosenberg
DOI: 10.1115/1.3636501Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: A system of n masses, equal or not, interconnected by nonlinear “symmetric” springs, and having n degrees of freedom is examined. The concept of normal modes is rigorously defined and the problem of finding them is reduced to a geometrical maximum-minimum problem in an n-space of known metric. The solution of the geometrical problem reduces the coupled equations of motion to n uncoupled equations whose natural frequencies can always be found by a single quadrature. An infinite class of systems, of which the linear system is a member, has been isolated for which the frequency amplitude can be found in closed form.
keyword(s): Equations of motion , Degrees of freedom , Equations , Frequency , Linear systems AND Springs ,
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| contributor author | R. M. Rosenberg | |
| date accessioned | 2017-05-08T23:01:08Z | |
| date available | 2017-05-08T23:01:08Z | |
| date copyright | March, 1962 | |
| date issued | 1962 | |
| identifier issn | 0021-8936 | |
| identifier other | JAMCAV-25655#7_1.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/88879 | |
| description abstract | A system of n masses, equal or not, interconnected by nonlinear “symmetric” springs, and having n degrees of freedom is examined. The concept of normal modes is rigorously defined and the problem of finding them is reduced to a geometrical maximum-minimum problem in an n-space of known metric. The solution of the geometrical problem reduces the coupled equations of motion to n uncoupled equations whose natural frequencies can always be found by a single quadrature. An infinite class of systems, of which the linear system is a member, has been isolated for which the frequency amplitude can be found in closed form. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | The Normal Modes of Nonlinear n-Degree-of-Freedom Systems | |
| type | Journal Paper | |
| journal volume | 29 | |
| journal issue | 1 | |
| journal title | Journal of Applied Mechanics | |
| identifier doi | 10.1115/1.3636501 | |
| journal fristpage | 7 | |
| journal lastpage | 14 | |
| identifier eissn | 1528-9036 | |
| keywords | Equations of motion | |
| keywords | Degrees of freedom | |
| keywords | Equations | |
| keywords | Frequency | |
| keywords | Linear systems AND Springs | |
| tree | Journal of Applied Mechanics:;1962:;volume( 029 ):;issue: 001 | |
| contenttype | Fulltext |