MATEC Web Conf.
Volume 211, 2018The 14th International Conference on Vibration Engineering and Technology of Machinery (VETOMAC XIV)
|Number of page(s)
|NC: Nonlinear Dynamics and Control of Engineering Systems; TP1: Non-linear vibrations
|10 October 2018
Nonlinear free and forced vibration of Euler-Bernoulli beams resting on intermediate flexible supports
Laboratoire de Mécanique Productique et Génie Industriel, Ecole Supérieure de Technologie, Hassan II University of Casablanca,
2 Mohammed V University in Rabat, EMI-Rabat, LERSIM, B.P.765 Agdal, Rabat, Morocco
This paper deals with the geometrically nonlinear free and forced vibration analysis of a multi-span Euler Bernoulli beam resting on arbitrary number N of flexible supports, denoted as BNIFS, with general end conditions. The generality of the approach is based on use of translational and rotational springs at both ends, allowing examination of all possible combinations of classical beam end conditions, as well as elastic restraints. First, the linear case is examined to obtain the mode shapes used as trial functions in the nonlinear analysis. The beam bending vibration equation is first written in each span. Then, the continuity requirements at each elastic support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. Numerical results are given to illustrate the effects of the support stiffness and locations on the natural frequencies and mode shapes of the BNIFS. The nonlinear theory is then developed, based on the Hamilton’s principle and spectral analysis. The nonlinear beam transverse displacement function is defined as a linear combination of the linear modes calculated before. The problem is reduced to solution of a non-linear algebraic system using numerical or analytical methods. The nonlinear algebraic system is solved using an explicit method developed previously (second formulation) leading to the amplitude dependent nonlinear fundamental mode of the BNIFS.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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