Abstract
When a nonlinear system having several masses vibrates in normal modes, the time histories of the motion of these masses are, in general, different in wave shape (although in certain special nonlinear systems they differ at most in amplitude, but not in shape). When the wave shapes differ, the normal mode vibration is called nonsimilar. In this paper, nonsimilar normal mode vibrations are analyzed with respect to wave shape and stability. The systems considered are those lying close to systems having similar normal mode vibrations. An example is worked out in detail, and a comparison with an experimental study is reported.
Highlights
INseveral earlier· papers [J, 2, 3, 4), 1 t he normal mode vibrations of certain nonlinear systems, having many degrees of freedom, have been studied. These systems consist of a chain of masses, each mass having a single degree of freedom of translaLion in the direction of the chain
Each is connected to others by nonlinear springs, and every spring force is an odd function of t he length change of that spring
If we denote the velocity of the unit mass by w, we find from the energy integral !w2 = U + h that the transfer time along any trajectory is for U and w and for their partial derivatives, standard perturbation technique yields the equation which 1J(x ) must satisfy
Summary
Nonsimilar Normal Mode Vibrations of Nonlinear Systems Having Two Degrees of Freedom. Journal of Applied Mechanics, American Society of Mechanical Engineers, 1964, 31 (2), pp.283290. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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