Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

non-linear vibration Related Publications

3 Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint

Authors: F. Rahimi Dehgolan, M. Najafi

Abstract:

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Stability, bifurcation, non-linear vibration, axially moving beam, multiple scales method

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2 Super Harmonic Nonlinear Lateral Vibration of an Axially Moving Beam with Rotating Prismatic Joint

Authors: F. Rahimi Dehgolan, S. Bab, M. Najafi

Abstract:

The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: Galerkin Method, super harmonic resonances, non-linear vibration, axially moving beam

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1 Geometrically Non-Linear Free Vibration Analysis of Functionally Graded Rectangular Plates

Authors: El Bikri Khalid, Benamar Rhali, Boukhzer Abdenbi

Abstract:

In the present study, the problem of geometrically non-linear free vibrations of functionally graded rectangular plates (FGRP) is studied. The theoretical model, previously developed and based on Hamilton’s principle, is adapted here to determine the fundamental non-linear mode shape of these plates. Frequency parameters, displacements and stress are given for various power-law distributions of the volume fractions of the constituents and various aspect ratios. Good agreement with previous published results is obtained in the case of linear and non-linear analyses.

Keywords: functionally graded materials, non-linear vibration, rectangular plates

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