Nonlinear Vibrations of Bimodular Continua by Means of Isogeometric Analysis

Abstract

The modeling and numerical analysis of the dynamic response of originally straight homogeneous Bernoulli-Euler beam rigid in shear with classical boundary conditions under time-varying excitation are studied. However, the beam is composed of a bimodular material, thus behaving differently in tension and compression. This implies that the neutral axis does not pass through the geometric centroid of the cross-section and depends not only on the elastic material properties but also on the curvature’s sign and the geometry of the cross-section. Within this study, an isosceles triangular cross-section is analyzed, showing a difference in neutral axis position between positive and negative curvature with respect to the modular ratio. The governing equation for flexural oscillations of the bimodular beam is formulated based on the model with effective two-layer laminates and discontinuous natural beam axis with respect to the axis through the cross-section’s geometric centroid, which is used as an independent reference axis of the bimodular beam structure. The numerical analysis of the dynamic response of the bimodular beam is investigated by means of isogeometric analysis (IGA). The fundamental idea behind isogeometric analysis is to use the same basis functions for constructing the exact original geometric model and for approximating the unknown solution fields. Finally, a numerical study is given to verify the effectiveness of the isogeometric approach on the dynamic analysis of the bimodular beam.