Nonlinear dynamics of a vertical cantilever beam under biaxial base excitation

The objective of this manuscript is to investigate the dynamic behaviour of a nonlinear vertical beam under base excitation applied at different angles. An inverted cantilever beam with a tip mass is considered. This study aims to analyse the system's diverse dynamic responses under different excitation parameters, which hold potential for various practical applications. 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 for near-buckling and post-buckling conditions. Furthermore, by carefully selecting excitation angles, amplitudes, and frequencies, the system configuration can be tuned to monitor response amplitudes, enabling tailored performance optimised for specific dynamic requirements.