On nonlinear vibrations of systems with many degrees of freedom

Reinhardt Rosenberg (1)

1 Department of Mechanical Engineering [Berkeley]

The study of the vibrations of nonlinear systems with many degrees of freedom is concerned with the search for some or all periodic solutions of systems of nonlinear differential equations and to deduce as many properties of these solutions as the state of the applicable mathematical knowledge permits. Unfortunately, this body of knowledge is limited and not unified; in consequence, many and vaned disciplines within mathematics are commonly used to deduce partial results. In a general way, these results fall into two broad categories: those which apply to systems that are “weakly nonlinear,” and those which apply when the systems are “strongly nonlinear.” The results in the first category contain a good deal of detailed information, and they resemble in many ways those familiar from linear theory. Those in the latter category usually contain fewer details, being more concerned with general questions of existence, uniqueness, boundedness, and stability of solutions.

Domaines: Mécanique [physics]

Reinhardt Rosenberg. On nonlinear vibrations of systems with many degrees of freedom. Advances in Applied Mechanics, 1966, ⟨10.1016/S0065-2156(08)70008-5⟩. ⟨hal-01544496⟩