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The Normal Modes of Nonlinear n-Degree-of-Freedom Systems

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.
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Submitted on : Tuesday, July 12, 2016 - 2:11:30 AM
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Reinhardt Rosenberg. The Normal Modes of Nonlinear n-Degree-of-Freedom Systems. Journal of Applied Mechanics, American Society of Mechanical Engineers, 1962, 29 (1), pp.7-14. ⟨10.1115/1.3636501⟩. ⟨hal-01344457⟩

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