This study presents a mechanical model and numerical analysis of the dynamic response of a homogeneous Bernoulli-Euler beam, which incorporates classical boundary conditions and is subject to time-varying excitation. However, the beam is constructed from a bimodular material, characterized by differing Young’s moduli in tension and compression. This material property results in the neutral axis not passing through the geometric centroid of the cross-section, with its position dependent on the sign of the curvature. Consequently, the equation governing flexural oscillations is formulated using a model that involves effective two-layer laminates and a discontinuous neutral beam axis. Each of the two bending configurations is uniquely characterized by its neutral axis position, which is influenced not only by the elastic material properties but also by the geometric characteristics of a cross-section. Depending on the cross-sectional properties, the dynamic response of a bimodular beam may exhibit either linear or nonlinear behavior. When a difference in effective bending stiffness exists between upward and downward bending, deriving an exact closed-form solution for the entire motion domain expressed by a single equation becomes impossible. Therefore, isogeometric analysis is applied to provide an approximate solution, not just for linear but particularly for nonlinear vibration of a bimodular beam. The modified Newmark method is used to analyze responses in the time domain, while the harmonic balance method is specifically applied to investigate the frequency-response function to periodic excitation, emphasizing nonlinear bimodular beams. Finally, a numerical study is conducted to validate the efficacy of the isogeometric approach in the dynamic analysis of bimodular structures. A comparative analysis of the responses highlights the considerable impact of bimodular materials, particularly concerning their cross-sectional properties.