Nonlinear Normal Modes of a Parametrically Excited Cantilever Beam |
| |
Authors: | Yabuno Hiroshi Nayfeh Ali H. |
| |
Affiliation: | (1) Institute of Engineering Mechanics, University of Tsukuba, Tsukuba-City, 305-8573, Japan;(2) Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, U.S.A |
| |
Abstract: | We investigate theoretically thenonlinear normal modes of a vertical cantilever beam excited by aprincipal parametric resonance. We apply directly the method ofmultiple scales to the governing nonlinear nonautonomousintegral-partial-differential equation and associated boundary conditions.In the absence of damping, it is shown that the system has nonlinear normal modes, as defined by Rosenberg, even in the presence of the parametric excitation.We calculate the spatial correction to the linear mode shapedue to the effects of the inertia and curvature nonlinearities andthe parametric excitation. We compare the result obtained withthe direct approach with that obtained using a single-mode Galerkindiscretization.The deviation between the two predictions increases as the oscillationamplitude increases. |
| |
Keywords: | nonlinear normal mode parametric resonance mode shape direct approach Galerkin method discretization |
本文献已被 SpringerLink 等数据库收录! |
|