Nonlinear motion of a beam

Abstract

The investigation reported herein analyzes the vibration of a uniform beam with hinged ends which are restrained. The beam is subjected to a linearly-varying distributed load which has a maximum intensity w~ at the center and is released from rest when the load is suddenly removed. The motion is found to be inherently nonlinear, even for small vibrations, and there is dynamic mode-coupling. The mode frequencies are functionally related to initial conditions, particularly the amplitudes of all modes.

On the stability of prestressed beams undergoing nonlinear flexural free oscillations

“…Following [20][21][22][23] (see also [24][25][26][27][28][29][30][31][32]), we consider a hinged-hinged beam of length L (figure 1), mass density , cross-sectional area A, moment of inertia I and Young's modulus E, under an axial force N 0 (possibly also negative entailing compressive stresses). It turns out that the deflection w(τ , ξ ) at ξ ∈ [0, L] and time τ ∈ R is the solution of the following Mettler equation of motion 3 :…”

Comparison of the Von Kármán and Kirchhoff models for the post-buckling and vibrations of elastic beams

“…Comparison of the Von Kármán and Kirchhoff models for the post-buckling and vibrations of elastic beams amplitude-frequency dependence of extensible elastic beams in the weakly nonlinear regime, see for example (Ray and Bert 1969;Lou and Sikarskie 1975;McDonald 1991;Nayfeh and Mook 1995;Nayfeh and Emam 2008;Thomas et al 2016) and references therein. Furthermore, exact solutions have been derived for the Woinowsky-Krieger model (Nayfeh et al 1995).…”