On the dynamics of a slender cantilever having geometric nonlinearity under harmonic excitation with friction effects

This study explores the dynamics of a geometrically nonlinear, slender beam subjected to harmonic base excitation with friction effects at the excitation side. A mathematical model is developed using the Euler-Lagrange formulation and the assumed modes method, employing a two-mode approximation. Numerical simulations demonstrate that friction at the excitation side significantly affects the system’s behavior. In particular, the frequency response exhibits multiple jump phenomena and hysteresis regions over a broad excitation frequency range, with pronounced changes in steady-state amplitude levels. The response is further marked by enhanced higher-harmonic content in the spectral domain, indicating friction-induced redistribution of vibrational energy. The findings offer new insights into the nonlinear dynamics of flexible beam structures and establish a foundation for enhancing the analysis, design, and control of engineering systems where frictional effects are important.