ON NONLINEAR MODES OF CONTINUOUS SYSTEMS

We use several methods to study the nonlinear modes of one-dimensional continuous systems with cubic inertia and geometric nonlinearities. I nvariant manifold and perturbation methods applied to the discretized system and the method of multiple scales applied to the partial-differ ential equation and boundary conditions are discussed and their equiva lence is demonstrated. The method of multiple scales is then applied d irectly to the partial-differential equation and boundary conditions g overning several nonlinear beam problems.