The Normal Modes of Nonlinear n-Degree-of-Freedom Systems
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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.
1982 ◽
Vol 24
(4)
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pp. 163-171
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1960 ◽
Vol 64
(599)
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pp. 697-699
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Keyword(s):
2017 ◽
Vol 17
(02)
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pp. 1750019
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