Non-linear oscillations of a thin-walled composite beam with shear deformation

2Citations
Citations of this article
10Readers
Mendeley users who have this article in their library.

Abstract

A geometrically non-linear theory is used to study the dynamic behavior of a thin-walled composite beam. The model is based on a small strain and large rotation and displacements theory, which is formulated through the adoption of a higher-order displacement field and takes into account shear flexibility (bending and warping shear). In the analysis of a weakly nonlinear continuous system, the Ritz's method is employed to express the problem in terms of generalized coordinates. Then, perturbation method of multiple scales is applied to the reduced system in order to obtain the equations of amplitude and modulation. In this paper, the non-linear 3D oscillations of a simply-supported beam are examined, considering a cross-section having one symmetry axis. Composite is assumed to be made of symmetric balanced laminates and especially orthotropic laminates. The model, which contains both quadratic and cubic non-linearities, is assumed to be in internal resonance condition. Steady-state solution and their stability are investigated by means of the eigenvalues of the Jacobian matrix. The equilibrium solution is governed by the modal coupling and experience a complex behavior composed by saddle noddle, Hopf and double period bifurcations. © 2013 Elsevier Inc.

Cite

CITATION STYLE

APA

Machado, S. P., Saravia, C. M., & Dotti, F. E. (2014). Non-linear oscillations of a thin-walled composite beam with shear deformation. Applied Mathematical Modelling, 38(4), 1523–1533. https://doi.org/10.1016/j.apm.2013.08.028

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free