Nonlinear Dynamics of a Vertical Cantilever Beam Under Biaxial Base Excitation

Abstract This study investigates the dynamic behavior of a vertical cantilever beam with tip mass under biaxial base excitation. Excitations are considered along the axis of the beam (vertical) and in a transverse direction (horizontal). Diverse dynamic responses of the system are reported for different excitation parameters. The horizontal excitation remains external, whereas the vertical excitation provides parametric excitation to the system. The tip mass shifts the vertical beam from a linear to a nonlinear regime. Numerical simulations are carried out to understand the behavior at pre-buckling, near-buckling, and post-buckling conditions. Results from the combined loading show distinct dynamical behaviors including periodic, quasi-periodic, and chaotic responses.