Istituto di Scienza e Tecnologie dell'Informazione     
Kharenko D., Padovani C., Pagni A., Pasquinelli G., Semin L. Free longitudinal vibrations of bimodular beams: a comparative study. In: International Journal of Structural Stability and Dynamics, vol. 11 (1) pp. 23 - 56. World Scientific, 2011.
In this paper, we consider the problem of the free longitudinal vibrations of a beam made of a bimodular material, i.e. an elastic material whose in-tension Young's modulus is a fraction of that under compression. After recalling the exact solutions for an infinite beam and for a beam with fixed ends calculated via the characteristics method, we apply high-resolution methods based on the finite-element approach to solve the nonlinear equation of the motion. In particular, we compare the exact solutions with the numerical solutions calculated using the collocation and least-squares method developed in the present study, the space-time element method, as well as total variation diminishing (TVD) and Newmark methods.
URL: http://www.worldscinet.com/ijssd/11/1101/S02194554111101.html
DOI: 10.1142/S0219455411003975
Subject Bimodular material
Nonlinear dynamics
Exact solutions
Numerical solutions
J.2 Physical Sciences and Engineering

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