Abstract: We use several methods to study the nonlinear modes of one-dimensional continuous systems with cubic inertia and geometric nonlinearities. Invariant manifold and perturbation methods applied to ...

Abstract: An experimental study of the response of axially-symmetric (i.e., circular cross-section) cantilever beams to planar external excitations is presented. Because of the axial symmetry, one-to-one ...

Abstract: We use two approaches to determine the nonlinear modes and natural frequencies of a simply supported Euler-Bernoulli beam resting on an elastic foundation with distributed quadratic and cubic ...

Abstract: Two approaches for determination of the nonlinear planar modes of a cantilever beam are compared. In the first approach, the governing partial-differential system is discretized using the linear ...

Abstract: A complex-variable invariant-manifold approach is used to construct the normal modes of weakly nonlinear discrete systems with cubic geometric nonlinearities and either a one-to-one or a three-to-one ...